I highly recommend checking out Notre Dame cathedral - not for the tourist trap value, but if you're there on a Sunday, they have an organ performance at 4pm every single Sunday. The plaster-shaking organ combined with the gorgeous acoustics and aesthetic of the catedral itself is breath-taking. Worth spending an hour. I made it every Sunday I could, even though
the church in my own neighborhood was a heck of a lot closer. +1 on renting a bike and exploring the city. The city is huge, and tons of neat alleyways, tiny streets, excellent under-trafficked cafes and neat architectual and cultural finds throughout the city. There are museums tucked away in what look like private homes, stores selling awesome things at great prices in back alleys and neat people to meet all around. I also recommend taking some time to stroll in the "
jardins des tuileries" and grab an espresso and a chair at one of the little cafes. It will be gorgeous in the Fall. Stroll through
Les Invalides. If you take the metro, I recommend getting off the line 8 at
La Tour-Maubourg and patroning the crepe stand kiddy-corner to the metro exit escalator -- great guy, wonderful crepes, cheap prices, no tourists. Plus, the absolutely beautiful stroll from there to Les Invalides is worth the 5-minute walk. You can eat your warm Nutella Banane crepe (highly recommended) while you walk. Really, there's a LOT to Paris that is just downright awesome outside of the touristy areas. Spend your few days there getting the chance to scrape the surface of what Paris and Parisian life is really like and you'll enjoy it a lot more than having sat on tour buses driving by monuments, statues and building edifices while hurriedly snapping photos of and in front of buildings you know nothing about and will forget in a week. YMMV.