But sure nobody likes Americans?! Nah, just messing with you, some will like you, some won't - it won't really have much to do with your nationality, but the following: your attitude, your manners and, in the particular case of Americans, your decibel level.
Regarding attitude and manners: Italians are very friendly and hospitable, and many speak English reasonably well, but don't expect every single Italian person you meet to be fluent in English. If you travel there with a positive attitude, sense of humour, patience and good manners, you'll be fine. You might not remember how to say 'thank you' in Italian, but if you make eye contact with the person, smile and say it in your own language, they'll understand. If you want to learn a few phrases in Italian, good ones to start with are Hello, Goodbye, please, thank you, Do you speak English and The food is delicious. Nobody will be offended that you try, and it can open doors, and make you new friends.
With regard to the decibel level: just talk a little quieter. That's all.
Things like what to wear: No polyester. Wear nice cotton and linen clothes, and be aware that if you are going into places of worship, you must cover your shoulders, chest, waist and legs. If you are going to be doing a lot of walking, you really should consider investing in some good walking shoes with proper arch support. Your knees, hips and back will thank you later.
PDAs are fine, up to a point - hugging and kissing in the street is perfectly acceptable, but please do not have sex in public places like parks. That sort of carry-on will get you arrested, even after dark. People here do have kids, remember.
The best conversations I have ever had have been with strangers. Also in Italy, and in some case we had a lovely great big language barrier to deal with! You can chat with strangers, but obviously you're not going to get into conversation with people who seem suspicious. And of course you can ask for directions. Again, the positive attitude and good manners should come into play.
Food and drink is more expensive in Italy than in the US, yes. Expect smaller portions, but they will taste very different, as fresh produce is considered the norm. Eat at trattoria, family-run places that might not be as fancy, but the meals are easily as good, if not better than the fancier ristorantes. Be advised that if you are just calling for a coffee, if you sit at a table and then order it, you could very well be hit with a service charge on top of the coffee, especially in touristy areas. Do what the locals do, order your coffee 'al volte' at the counter, drink it at the counter, and leave. Trust me, you only need make this mistake once to learn. Oh, and in the summertime, Italians tend to eat very late at night, usually not before 9 pm, but eateries will be open from about 5 or 6 to cater for tourists. What is nice about Rome is that there are public taps everywhere where you can simply fill up your water bottle - the water is perfectly good, and free.
Travel by train between cities, buy your tickets the day before. If you are not an experienced driver, you probably won't be allowed hire a car anyway, as there is an age limit. And to honest, having driven in Italy, I would not wish the traffic there on any novice driver, particularly in the south. Italians are lovely, friendly, gentle people, but they transform into total lunatics once behind the wheel of a car. Seriously, the best way to describe the traffic in Italy is as a spectator sport, and there are only two kinds of pedestrians: the quick and the dead. I would advise AGAINST it, and to ask at the tourist office in the city if there are any tours of vineyards - that way you can get out there, have a few drinks while there, and hiccup your way back onto the coach and not have to worry about drink-driving.
I don't know Verona, but Rome has a pretty extensive public transport system, with buses and a metro, or underground train. You can buy passes that last several days to use on this system. Like every public transport system in every city around the world, petty thieves and pickpockets are rife. If you're carrying a backpack, take it off and hold it in front of you. If you carry a handbag, make sure the strap is sturdy, across your body and that you can hold your hand over the opening. You just don't make it easy for them.
Now, I've shared my experiences with you, and I advise doing more yourself. Get yourself down to your public library, go to the travel section and borrow books on Italy, specifically Rome and Verona, and READ them. If you really do have your heart set on visiting vineyards, you can always google them, get an e-mail address and send them a mail asking if there are any tours organized from Rome or Verona to get to their properties, and could they possibly send you the contact details.