Paris is HUGE, but we tried to dedicate day 2 to see all the good touristy sites you want to see. We used the metro to get around, but I'd also recommend the classic hop on hop off tours if you don't have a lot of time in the city. First of course, we headed to the Eiffel tower. You can pay a few euros to either walk up or take an elevator up to the top and grab a drink looking over all of Paris. Its situated in a really nice stretch of greenery and park where you can have a great picnic under the tower. I recommend sunset or even an evening visit to see it sparkle!
After the tower, we headed to the Lourve. Buy your tickets in advance as they sell out pretty frequently. The Lourve is huge and you could spend an entire day there alone, but we opted for a couple hours. Of course, we had to see the Mona Lisa - but usually there is a HUGE crowd and it can be hard to see it, so be patient.
After the Lourve, we made our way to the Arc de Triomphe. You can also go to the top of the Arc (for free, I believe) through a tunnel that runs right under it. Careful of the crazy drivers! After this, on the main street that runs into the Arc, there is a ton of shopping and great restaurants. We ate at one right on the strip for dinner and it was delicious! Paris actually has really good pizza, if you can believe it. If you're there during November or December, they usually have a small Christmas market at the end of the main strip.