You're right about the US size being an 8. Usually the size would be M, sometimes can be considered small if you're looking for tops, especially.
Store-wise I would recommend going to Macy's, Ann Taylor LOFT, Forever 21 (definitely), and Express. These stores are usually great for finding a lot of new trending fashion if you're not worried about pricing (although Forever 21 isn't as expensive, but the clothes are amazing!)
If you go out to eat, definitely ask for a box for your portions that you're cutting out. In America, practically everyone does it, so it isn't a big deal, at all.
Restaurants I would recommend are Applebee's (which also is Weight Watchers friendly, they show calories on certain items) and Olga's Kitchen (especially if you like lamb and salads.)
If you're nervous about eating out, just be careful about the portions and when they ask if you want sides, etc. Most places usually recommend french fries for sides, but I swap it with salads when I can. They will definitely left you do that.
Good luck on your trip!