WyoPrincess,
In Galeries Lafayette (yes, a large dept. store) look up at the beautiful ceiling. On the rooftop get a good view of Paris. It is also very close to the Opera Garnier, a beautiful (rococo?) building. I highly recommend a tour of the inside, and perhaps a show or concert there if possible.
In Montmartre on the steps of the Basilica of Sacre Coeur, look out over a good view of Paris from here as well. Go inside the church...only just over 100 years old but filled with beautiful mosaics. Very touristy and overpriced (IMHO) a show at the Moulin Rouge ( perhaps the cabaret you seek?)
Definitely the Rodin Museum. Go before visiting the Eiffel Tower. It's a shortish walk from one to the other. The sculptures in the gardens are wonderful. I go there every single time I am in Paris. Give the gardens 1-2 hours. You can also go inside his house. Interesting, but missable with a short time involved.
The one hour boat ride on the Seine by Vedettes de Pont Neuf (inexpensive, narrated, usually in French, sit up top for best views). Get there about 45 min. before your time. It's at one end of the Ile de la Cite. Don't know about speakeasy's. Did they come up on Trip Advisor, and were they sponsored? Sounds touristy and gimmicky to me, but I don't know.
In Reims don't miss the cathedral (great stained glass and it is the place where nearly every French king was crowned). Also while in Reims you can visit the Musee de Rendition, where the surrender by the Germans for WWII was signed. A nice little museum.
Do you mean bicycle all the way to Versailles from Paris, or bicycle within the grounds of Versailles? The former seems too far, and I don't know how scenic it would be. The grounds are huge, so a bicycle within them is a good idea. This would be a full day trip. No tour group necessary, but take an early train there and on return you could do the boat ride on the Seine.
Favorite free thing to do is walk along the left bank side of the Seine and check out the bouquinistes. Lots of secondhand books, posters, whatnots, etc. (not clothes). Classic French experience, and offering a good view of Notre Dame as well. Speaking of ND, it opens December 8. Be sure to see Ste. Chappelle. It is close to ND. That is a don't miss for anyone! They have concerts there too, if you want to spend a bit.
I don't know about the Museum Pass and its usefulness in your situation. Just be aware you need to make reservations for Versailles palace, Ste. Chappelle. Rodin and Opera Garnier, I don't know.
Giverny you can take the train on your own. I would also go early to avoid big crowds. A little bus goes from the train station to Monet's house (and back, coordinated with train times). This could be a half or three-quarter day trip, giving you a late afternoon free for whatever you want to do (show, concert, boat ride?)
You have lots of options. Just be sure to check everyplace you are considering to see if you need to reserve a time. Walk-ups are mostly a thing of the past. Have a wonderful time!