Must see Paris can fill weeks! My own favorite museum is the D'Orsay. An easy walk across the river from the Louve. One of the stary night versions is on permanent display and it's approachable size is great compared to the Louve.
An alternate cathedral would be the Sacred Heart bascilica at Montemarte. Especially fun at sunset when people are hanging out on the steps and a quick ride up and down the funicular to a variety of neighborhood cafes.
An arch tour is always fun to get different perspectives from all three main arches that are all oriented in a single line starting at the Toularies Gardens, then the Arc De Triumph, and finally the Grand Arc at La Defense.
Hanging out on the weekend in Toularies garden is fun, as is strolling through the art gallaries in St. Germain. Marais is an interesting neighborhood from historical and current shopping / dining perspectives.
On and on it goes... Paris is truly one of the world's greatest cities. You'll run out of time on your visit before you run out of things to do and experience. Finally, if you are on your own and on a short time budget, the tourist bus is a great way to get around and take in the major tourist sites.
Mrygirl - I agree with you regarding the Batobus. It is a great way to see the river and get between some of the major sites at low cost. Like Paul Motter, I also had a great time in Versaille - both at the palace and in the open air market up from the train station on Sunday.