I did the same this summer and found that it was just as easy to stay at a hotel in St Michel since I was going into the city anyway and didn't have all that much luggage.
Transport to the airport from St Michel is easy enough because the RER is right there, and for such a short time I didn't want to mess with shuttle to hotel, then to RER, then into city...
As for what to do: depends on whether you've been to Paris before and what you like. It's a great walking city, and walking around is a great way to reset your body clock. I might just do Notre Dame, St Chapelle, Louvre, and maybe a walk near the Opera Garnier.
PS Note: I think it might be possible to check your bags through to your final destination and then only carry on/have in Paris what you need. It's worth checking, because it's much easier if you can avoid the baggage claim, checking bags back in, hauling them in Paris, etc.