Cafés are great places to relax while you're traveling, and if you can find an Internet café, that's all the better -- you can get work done, too. It's a good idea to research your destination before you head out, so you'll know where the most convenient Internet cafés are located.
If you want to immerse yourself in a local culture, find a nice café. The food is filling and almost as fast as fast food, the conversation is usually free flowing, and most cafés don't care how long you hang out. Best of all, they're easy to find and easy on the pocketbook.