I know this sounds stupid, but one of the most fun things to do in rome is to go look through a pretty decent amount of travel stuff you like and generally respect: nytimes 36 hours, travel section, anthony bourdain, look at some other travel guides. And find good trattorias, cafes and bars. Then plan some walks and stop in at 3 places for coffee or drinks and do some shopping in between. There is always a little shop, bar, cafe that you can stop off for a glass of wine at or a cup of espresso. Spending time in a semi-structured environment where you don't have anything to do really, but you have an idea of where you are going generally and where things are relatively is the most enjoyable way to experience a place in my opinion, particularly with your lover.
