I've had a number of pairs of Birkenstock Mary Janes over the years and they are great for walking (pricey, though)

I have worn black Tiek ballet flats Tieks for many long hours of walking, standing, etc. and they have worked well. Plus they are not ugly. I also own a pair of Puma Zandy ballet flats that have served me in the same capacity. They are sold out at Nordstrom, but I found them on Amazon: Puma

Ballet flats killed my toes after long days on concrete.

Maybe some cute flat ankle boots? I just bought a pair from Born and the sole is nicely cushioned and supportive. Careful, because too many boots don't have insoles.

I just found amazing sneakers at Costco! I bought a pair in black and ordered them also in gray(although they look more silver) because I liked them so much. I then ordered two more to save as it is so difficult for me to get comfortable shoes.

They are the Puma Vikky Mesh. I ordered 1/2 size up. I was able to try them on in the store so my usual shoe size was too small. 1/2 up was great. I think they look cute with leggings, ankle jeans, and shorts.

ETA: I have a small, wide foot with a high arch, so finding comfortable sneakers and shoes is a feat (pun intended) for me.

I bought the Sketchers this summer because I wanted an alternative to sneakers and Easy Spirit mules. I really like them.

I've also seen Birkenstock sneakers that look similar to the Pumas above. They're pricey but look good. I like the metallic ones.

http://www.birkenstock.com/us/shoes/women/sneakers/

I have a pair of Naturlizer shoes called "Famke" that are amazingly comfortable even when on my feet all day. I haven't worn them hiking, but have worn them for long walks, art fairs, and treks around hospitals. I wear them with a toe-sock (that little thing that just covers the toe and ball of foot).

I'm a moccasin girl. Mine come from Minnetonka.

https://www.minnetonkamoccasin.com/

Eld, speaking of Costco ... I recently bought a pair of Ugg knockoffs online for $29. They are unbelievably comfortable!

https://www.costco.com/Kirkland-Signature-Ladies'-Shearling-Zipper-Boot.product.100332608.html

I have these Taos Mary Janes and they are great for walking without being too dorky. At the price listed in the link, they are a steal if they have your size. I find that Skechers are too squashy for walking on pavement.

taos mary janes

Love Flexx! They're Flex-y. Utilitarian with a spin.

https://www.theflexxusa.com/

Wow, thanks so much for these great suggestions! The Skechers slip ons are on sale at Macys so I'm going to check them out ASAP. The Puma shoes look very promising too.

Actually my summer walking shoes are Skechers which I've worn the last few times I was traveling in warm weather and they are a dream. If anyone's looking for super light comfortable shoes that are a dream for hoofing around all day, you might want to check these out.

Back before I developed a bum foot (hallux limitus), I had good luck with keens and echos. I'm a fan of zappos. I order four or five pairs, keep what works, then ship the rest back for no additional cost.

There is a lot of walking in DC and you will see many many people wearing running'/walking shoes. If you don't find anything that appeals to you you certainly won't look out of place wearing your most comfortable shoes.