I am planning a trip with my girlfriend (both early 20s) this coming June. We have about 10 total days of vacation (2 of them flying) and we have set our sights on Rome, Venice, and the Amalfi Coast. I've seen several topics similar to mine, but none with these exact cities and age range. We are probably not as into the historical aspect as most, but will definitely make time for sightseeing. We enjoy outdoorsy things and quality food/drink.
I was hoping I could get a few travel tips in terms of (1) what to absolutely make sure we do in each city (2) what might not be worth it for the amount of time we have (3) recommended places to stay and (4) any other tips that you guys have picked up on during your travels. Also, any other do's and don't as far as Italian customs/manners would be appreciated. Our budget after airfare is probably between 1.5k-3k each all in (1.5 being "optimistic", 3 being "hopefully not").