Ah, I'm so jealous!. I need to go on an exciting vacation sometime soon.
I know you said you didn't want to go the "running shoes" way when you are abroad, but honestly, what could be better than that? Maybe in DC everyone's wearing bulky weird sneakers and not cool ones and that's why it's given you a sour taste in your mouth. I'm a really big fan of Puma sneakers and every time I've had to do anything remotely outdoorsy in the past 10 years, I end up wearing my favorite sneakers. (Well, back then I wore sneakers everyday anyways, but still.)
Maya Satin Sneaker $30, Puma
They're super lightweight, breathable and have a good tread on the bottom. If these aren't really your steez, maybe you'd be more into the classic Adidas Samba style? They're suede so they won't be as breathable, but they're cuter and they'll definitely be just as comfortable.
Samba W Sneaker $60, Adidas
Having said that, these two sneaker styles are not my #1 choice for you. While I was on the Puma website, I came across a shoe that I think will really fulfill all your needs and beyond.
Zandy Ballerina Flats $70, Puma
Sneaker-y ballet flats can often be kind of weird, but these are made to brave the pavement so I think their weirdness is justified (and well-developed, I think these are actually really cute!). According to the website, they feature a "moisture-wicking lining and antimicrobial EcoOrthoLite (whatever that is) footbed for oder prevention and long-term cushioning," which sounds to me like they would be PERFECT for your travels. They come in a couple other colors, but I like the "quiet sophistication" of the putty color. Bonus! These will look really great with dresses too.
Also, I had to Google Keen sandals–YOWZA!–but, if they're really the best thing to travel in then I feel like you might have to forgo the cute shoe idea and bite the comfort bullet.
La Paz Strap Sandals $70, Keen
These aren't bad at all!
Except that the thought of traveling and doing a lot of walking with exposed toes (you knew it was coming!) in a FOREIGN country is making me hyperventilate extra. And there aren't socks cute enough that could ever make this look work. Proceed at your own risk!
I still think the lil' Puma flats are kinda the best thing ever, non?