One of my absolute favorite places in Paris is Montmartre. It's bustling with artists and tourists, great restaurants and small food carts. There is truly something for everyone. (And if you're a fan of Amelie, you'll recognize the area!)
The Sacre Coeur is my favorite building in Paris, and you can even climb to the top and see the ENTIRE city from an entirely new point of view. You can also go down to the crypts and get some of the history of the place. OR, buy some bread, cheese and wine and settle down on the steps in front and watch Paris from on high while munching.
It's beautiful both at night and during the day, so if you have time, make the trip a couple of times.