We just got back from a two week vacation and, in retrospect, we tried to do too much. We saw basically all of the most popular areas except for Cinque Terre (so I can't speak to that), and here is my personal take:
- Lake Como: Only go here if you are looking for relaxation and overpriced shopping. The surroundings are certainly beautiful, but it was a little too slow paced for me. Wish we had done some hiking here instead of boating around to the various towns that had very little to see.
- Milan: Skippable for a 10-day trip IMO, but definitely a contrast to the rest of Italy. If you fly in to Milan though, it could be worth spending 1-2 days there.
- Venice: Unique and romantic city with a fascinating history. St. Mark's, Doge's Palace, Canals, nighttime strolls, etc...Highly recommend 2-3 days here.
- Florence: If you are into art and sculpture, an absolute must see. My wife and I are not art history buffs, but we still thoroughly enjoyed Florence for its history. It also serves as a decent launching point for day trips into Tuscany which I highly recommend. I'd recommend 3+ days here (2 for Florence itself, and 1+ for day trips).
- Siena: We went here very briefly as part of a Tuscany day trip, but I wish we had spent longer because it seemed unique and interesting. That being said, your time is probably better spent elsewhere for a 10-day trip.
- Rome: If you haven't already been, Rome can't be missed. It has something for everyone--art, history, religion/culture, food, etc. Very easy to fill up 3 days here and could do more. If you do go, I highly recommend the Testaccio Supper Stroll (I found out about it on this board actually).
- Amalfi Coast: If you go here, you have to commit at least 3 days to it IMO. It is a major PITA to get there and can be a major PITA to move along it. However, it is beautiful and the Path of the Gods hike was one of my favorite things we did all trip.
Happy to answer specific/detailed questions if you have any. I think it largely depends on what types of activities you and your SO enjoy, and how "honeymooney" you want the trip to be.