Damn I'm jealous, I spent a weekend there with a "friend" and what they say about Paris being romantic is true.
Just remember that there are @ssholes anywhere, even in Denmark which was pretty supportive of the US there were some crazies.
Try having some wine by the Effiel tower at night, very gorgeous.
Take out dinner by the Sine river (I had some sushi which was suprisingly good with wine).
The hill that the Sacr Cour is on is very nice at night too, a bit touristy but nice cafes and a good view of the city.
Trains are fairly nice, you might look into getting a Eurorail pass if you plan on using it for any lenght of time.
Day trips (or spend the night there) to some big cities from Paris would be:
Amsterdam (5hours)
Brussels (3hours)
London (4hours?)
And of course you could go to Versailles
I would leave Italy alone, it'll take time to get there, plus there is so much to see that you'll probably want todo it on a different trip.