you can order cabs in reduced depth so on one side you have some storage, and feet and knees will be comfortable on the sitting side. You can use wall cabs in shorter heights and attach attractive feet/legs to bring the unit to the floor and support your counter. Cabinet companies have"island programs" now with assorted legs/shelving/columns/shelf support/small drawers/ etc. I'd try to get something going so it looks trimmed out and works with the rest of your kitchen.

yeah that would be Ideal, but I really can afford to take any more room in width. That is why Im going to use the 2x4 wall instead of cabinets. Im more or less trying to figure out what to do for the open end, that isnt attached to the wall.

No need to put anything below if you make it like a table attached to the wall. Just have 2 legs on the end away from the wall or a narrow "wall" to act as a leg if you a traditional style. If you use the same material coming down the side, it would like nice if you have any sort of modern vibe....
If it has a "thin" top, then you don't want to box in people's legs anyway....

Here is a link that might be useful:

Do you have a picture of the space you are talking about?
If you do not need storage why not use a small narrow
kitchen island or table?

I would love to offer up images but I am a bit confused.
Let me ask a few more questions.

Is this a pony wall? What was in the space before?
How narrow is the kitchen? What is the floor plan of the
kitchen?

Do any of these below help? If so I can try to find more.
~boxer

Table

This is a narrow area just for eating

My first thought was a console table you could move around out of the way. Perhaps turn it against the wall w/ your stools under it.

Then I remembered the low bathroom vanities everyone's getting rid of.

Then I realized you keep saying "2x4s" but what is the width you're looking for. If you said, I'm not getting it.

Those pics, as always, are inspiring!

The space is empty right now so taking a picture wouldnt help unfortunately. What I have is a small house with a small living room and the kitchen beside it, I took out the wall between the living room and kitchen and am re doing the kitchen. There isnt any room for a dining table, there never really was before either, so what I was planning is having a peninsula/bar to eat at. The peninsula would stick out where the wall used to be or a little bit towards the kitchen, to not take up any more living room space. SO the stools would be on the kitchen side. I have approx 8 feet for the peninsula so room for 4 seats.
I keep saying 2x4 wall because I cant use base cabinets, just cant afford the room. So Im thinking basically a pony wall with a bar top. Im just not sure on the best way to finish off the open end to give lateral support to the wall. Should I return the wall 90 Deg. and go the width of the top? Or just go with a gable and secure it really well. Or something else.
Im leaning more towards the return wall because it would be more support.
But Im completely open to other ideas. I can try and explain more if anyone needs.

Thanks for the help :)

Something similar to this, but It wouldnt be open undernieth, as I will probably have the couch backing on to the wall.

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[modern kitchen design[(https://www.houzz.com/photos/modern-kitchen-ideas-phbr1-bp~t_709~s_2105) by photographer Elad Gonen & Zeev Beech[/url]

I'm also trying to devise a peninsula for my kitchen, one that would look like the pictures in dianalo and Maceachhernb's postings, but I was told that since I'm using Caesarstone for the peninsula top, I had to devise some other support mechanism for hanging end since Caesarstone is not rated for vertical weight. I was thinking that I'd put two legs under the edge and build a Caesarstone box around them. Does this sound reasonable?? (Sorry if this is hijacking your post, Maceachhernb, but it sounds like we have similar issues!)

Okay, let me ask a direct question that may help. How wide do you want the surface of the peninsula countertop to be?

MIne will be 36" wide and 72" long