If you do want to go somewhere gorgeous and quite safe, go to the Rodin Museum near Invalides. The Rodin Museum has lovely gardens with lots of statues. It also has an area towards the rear of the gardens with lounge chairs that allow you to stretch out fully. My travelling companion became quite ill one afternoon while we were in Paris. It was nothing serious - just nausea combined with the need to lie down and rest. I toured the gardens while she took a quick nap. The fresh air, quiet atmosphere, and anti-nausea drugs worked wonders.

Currently the interior part of the museum, the house that includes Rodin's works of art, is closed. The admission price for the gardens is inexpensive. The gardens are secure; no one can gain entry without purchasing an admission ticket. There is a small restaurant or you may picnic in the gardens if you are discrete. Toilets are also available.

I would only say not go check out Sacre Coeur because of all the people.
I've been there once and by 830 it was filling up with groups. I had about 20mins with a few other people before it got slammed.

Anyways, I've only been to Paris once myself and am finally returning this fall. I'd say drop off your luggage (if you can) and then just walk around.
Have a coffee to try to get used to the local time.
I often have a 30-40mins nap and then force myself to go out. Sure I'm a bit groggy, but I haven no issues going to sleep at a normal time.

Thanks for the Opera site. Im def going to be checking that out!
I was on a student budget last time so I only was able to afford going up the Montparnasse tower.

Lots of museums close on Monday or Tuesday.
Getting to Sacre Coeur is all UPHILL--after a long flight I'd be more inclined:) to be on level ground. There is a funicular that will get you to SC.
There are several GRAND MAGASINS (department stores) a few blocks from the Opera--at the top you can get a panoramic view of Paris.

go to a wine bar, and have toast with foie grae, and a pot of burgundy.,

If I'm awake that sounds like a great idea. Just need to find a wine bar near the hotel.

Coffee ,Champagne ,Croissant. Chill
 

^^QUOTE=aamilesslave;24695732]The boat cruise or heading up to Montmartre & Sacré-Coeur is an excellent idea, especially if the sun is out. A walk through the Luxembourg Gardens would also be quite nice.[/QUOTE]

Just don't do that until 2-3 hours before you plan to go to bed ;)

That's not just a fun thing to do on the first day, but a fun thing to do the whole trip! ;)