I was just going to suggest florence to you! why if you have to go there don't you go then?? I have been to florence three times and would go again in a heartbeat, IMHO it is more romantic than paris, i find paris beautiful but a little on the cold, somber side, again that's just me. Florence is compact enough to be able to walk to most attractions and just have a very relaxing vacation. The food is excellent as well. You can also take a quick trip on the train to some neat small towns in the tuscan countryside.
If you are worried about cost, I think 3000 dollars is doabe as long as you stay in cheap hotels and maybe even in private rooms in hostels. I always stay in hostels in my vacations and have met many couples. You will have a blast!! great food, beautiful art and architecture and a very warm people to welcome you.
YOu can also think about venice, which is a bit more expensive or even rome which is not really romantic per se but it's my favorite european city by far