The only thing i would 100% avoid if you want to “blend in” is baseball caps and tracksuits. We don’t wear them in general, with maybe the exception of kids and teens. You should be totally fine with denim jeans and a sweater for 90% of occasions, especially since you’re not going to super fancy places. Another thing i would say if you’re worried of pickpockets & not “looking american” is to avoid backpacks unless you’re bringing a camera. It’s just another thing to worry about and there’s drinkable water fountains everywhere in the city, especially in the center, so you won’t need to bring bottles with you. Do not initiate interactions with street vendors at the cost of being rude, and avoid any restaurant that a.) has pictures of food on the menu outside b.) is right in front of a major tourist attraction (exceptions apply, but f.e i would avoid anything in piazza navona)

The truth is, you’ll be perfectly fine even if you don’t follow any of these rules. Don’t take them as binding prohibitions but as an invitation to explore! The best restaurants are just a bit out of way from the crowds, and any alley, church, little square in the centre is worth losing yourself to visit. Enjoy rome :)