Our local newspapers both run annual polls, "Best of the County" with maybe 100 categories. Check and see if your local papers do the same.

Printing out a form for them to fill out is definitely weird, in my opinion.
Casually asking about one or two of those things would be fine, and then you can see how responsive they are to helping you and proceed accordingly. If they're enthusiastic in their responses THEN maybe think about following up with a form.
But if a virtual stranger approached me with a questionnaire, I'd be put off.

sushipup that's a good Idea and I'll check that out.

greg I appreciate your candor - I was trying to put myself in their position and for me it would not be offensive, but everyone is different so that's why I asked here first. I have been to coffee with a couple of the women already so I'm not *quite* a stranger anymore but I see your point. I'll try a more low key approach.

Many subdivisions in our area have Facebook pages. It's a great place to ask questions of other residents. I've found several vendors that way -- both for home repairs as well as physician referrals and great places to hold birthday parties!

For every move, I ask my doctors to make referrals. They have worked out well. When I worked, people would gather to chat over lunch, and advice for favorite restaurants and plumbers was good. Our local True Value Hardware Store has great clerks, and DH will ask them for plumbing or whatever advice and when it goes beyond that, he will ask if they know of a good professional. They shop there too, and the clerks know them.

I remember my realtor offered many suggestions. If you had a good relationship, I think that he/she would be happy to make suggestions.
Just from knowing you here, you don't seem weird to me. In person, you especially wouldn't be weird.
For those who you kind of know, you can just put it put there. "As you know, we have recently relocated and I would love recommendations for a few things. They will probably offer more than what you need.
If you already have one doctor that you like, they can also recommend others to you.
As far as a hair stylist, I have asked strangers if I liked their color or cut! They are always flattered!

ellendi the only women I see are at the gym and their hair is not lookin' so good ! Obviously I need to get out more :-/ I have asked our realtors and got a great recommendation for an insurance agent but some of their other suggestions have not hit the mark for us. And thanks for saying I'm not weird!

If you've been out for coffee with these people, then that's different. I was just picturing someone who you've stood beside at the gym a few times and nodded hello to.

This is a smaller community, so maybe not as difficult.

I've been asked by strangers in the PO and the grocery store where I have my hair done, I'm happy to refer women with that...

If you find one good tradesperson, don't be afraid to discuss your other needs with him/her. I had an electrician here for an estimate and found him straightforward and personable. I had a concern about my dryer venting and asked him who I would call. I found a plumber I now treat as family ;) and asked him if he could give me a number to call to have the landscape sprinkling system reworked...he gave me three, and told me who he felt was the best choice of those. The clerk you buy those two gallons of paint from may have the name of a good small contractor or carpenter.

The dentist who lives across the street had a suggestion for a primary care doctor for DH, and we found ourselves at a party with the financial administrator to our hospital one evening who offered the same name...It all works out eventually, just stay attentive and don't be afraid to ask, or to ask why you're being told that provider would be a good fit.

See if there is a NextDoor in your area (or start one yourself)

Its a free, private social network for neighbors and your community.

Great place to find recommendations for a contractor/handyman, home repair services, hairstylist, dentist, doctor or even a dog walker, or quickly get the word out about any crime in the area.

Here is a link that might be useful: NextDoor

I've gotten my best advice about hair stylists when I was out shopping and passed a woman with a great cut and color and asked her who she used for her hair.

When we first moved here our neighbors had great suggestions for repairmen. Also as others above have said, Home Depot or the local hardware store employees have had good repairmen suggestions for me.

Urbanspoon has pretty accurate ratings for restaurants in our county. We've lived here over 20 years and still look at urbanspoon for new restaurants to try.

Our area has a magazine with the "best of" that would be a good starting point for doctors. I had good luck with asking neighbors.

For vet suggestions I would ask around at the dog park if you have one, or call a dog training facility if you have one and ask for recommendations. Or if there are any dog sports clubs or trainers, like agility clubs or trainers, they should have good vet contacts. If you are in a more rural area, the feed and seed store might have good suggestions.

You asked for suggestions about other things on the list to find. I would find an emergency vet pretty quickly, at least the number and location.

I live in a friendly area. I wouldn't hesitate to stop a friendly-looking woman my age in the grocery store, explain that I was new here and ask for suggestions. My neighbors were my go to source when we first moved here, though. The library is a good place to ask, too.

I hope you enjoy your new home.

See if there is a NextDoor in your area (or start one yourself)

Its a free, private social network for neighbors and your community.

Great place to find recommendations for a contractor/handyman, home repair services, hairstylist, dentist, doctor or even a dog walker, or quickly get the word out about any crime in the area.

Here is a link that might be useful: NextDoor

One of the small cities nearby has a Facebook page. It's not an "official" city page. It works pretty well for people to ask who's a good handyman, what pizza places deliver, is trash pick-up on schedule, etc.

It can get bogged down (as it did recently) with griping about snow plowing, or the slowness of same.

Look up a bunch of local real estate agents web sites. Some of them will have a Preferred Vendor List that they share.
Where did you end up moving to? Good luck with the new business and new town!

Since you've been to coffee with some of these women, they aren't complete strangers, so why not just ask them face to face. Next time you see them at the gym say "Hey, do you happen to know a good _________"

When we moved 5 states away a couple of years ago, Angieslist was a godsend. Worth every penny!

We have relocated several times on our marriage. You have to use what resources you have. I would talk to friends before moving, and use their contacts in the new place.

The 'net is full of recommendations for doctors or dentists that take no more than a Google search with location. Call the recommended docs to see if they take new patients.

It takes some time to find your stuff. Don't rush it. Take it one thing at a time. Find your doctor, your children's doctor, your dentist, etc.. as appointments are needed. Moving is a BIG deal. You need to form new relationships. They will happen before you know it.

I am a retired US Navy Submariner. The Navy moved my family and I about every 3-4 years. (This was all prior to the WWW being available in many homes.)

We relied heavily on co-workers for suggestions. Are you or your spouse still working?

I declined living in Military Quarters, preferring to own my own home and also to NOT live in a 100% Military Neighborhood. I found asking the folks "next door" for suggestions as to restaurants, tradesmen, etc.

Came back to give an update and see lots of new responses since I posted 2 months ago - thanks everyone.

I actually did type up and print a number of categories, gave it to a couple of women I'm getting to know and they offered suggestions for some of them. We found a great vet, I like my hair stylist, found an orthodontist I like and will probably use the dentist he recommends. Still have medical categories to fill in, can't get a decent manicure for some reason but that's no big deal, would like to find a reasonable upholsterer, and I would KILL for good Chicago pizza!!!

But for the most part, all is good considering we've been here 4 months and moved far from where we both grew up and lived our whole lives. It's an adjustment for sure, strangers in a strange land and all of that!! But it feels more like home every day and the days of feeling like 'what the heck did we do' are fewer and farther between. We're still renting a house, trying to find a house or property to build on and that's been a LOT more challenging than we anticipated. We find it takes a lot of our focus. Without realizing it we rented in a 55+ community and it's fine, people are nice but most are considerably over 55 and in a different phase of life than we are with different perspectives. Went to a New Years party (which ended at 9:30!) and we were the youngest by a good 20+ years.

I've joined a Meet Up group and will be attending a Trivia contest tonight (will try and drag my husband) so there are opportunities to meet other people and socialize.

To find a good doctor or dentist, I tell my previous one I am moving and ask for a recommendation. Sometimes they know someone good, but often they just check their directory that lists the degrees, schools, etc and can give you a good name.

My daughter likes to check out doctors and services on Yelp.

Were you in a sorority in college? Your local alumni chapter is a great opportunity to meet people and get recommendations.