There is a weekly Navigo pass that gives you unlimited bus and metro usage. The sticky bit is that the pass runs from Monday through Sunday. If you can get 5 days out of it, it's usually worth it. With 4 days, I'd get it because you're probably close to a break-even point and it is really nice to be able to hop on a bus even for just one or two stops, to save your feet . . . and in winter, perhaps to avoid some really cold or rainy walks. If it fits your plans, come back and ask for details. One (or more) of us will give you all the info you'll need.
December is Christmas season. Plan to enjoy the decorations and the special holiday markets. I wonder if it's worth going to Versailles in December for two reasons, first because of the short December days (sunrise around 8.30, sunset by 5.00) and also because the gardens may not be attractive in winter.
The Louvre is huge. Their website is excellent, so it's a good resource to choose what you most want to see there and then to plan a route through the building to see them. There's a section called "thematic trails" which has several self-guided tours that highlight different parts/aspects of the museum. It's open late on Wednesday and Friday, often much less crowded then. Their audio guide is very good - take a US driver's license with you to leave as security. The worst day to visit the Orsay and the Louvre is the day when the other one is closed, since the open one gets the overflow.
One way to avoid the lines at Sainte-Chapelle is to go to an evening concert. Go to the first performance, get there when the doors open and you'll have time to walk around the chapel and take photos. It's well-lit during the concert so choose seats in the middle or farther back to be able to view more of the stained glass while enjoying the music (usually light classical). BTW, the long line is for security, then either a short or no line for tickets. You can get concert tickets in other places than the ticket booth there.
The museum pass may not be worth it if you aren't going to visit a lot of the included sights. There are few that help you avoid lines - Louvre and Orsay for sure, but the long lines at the Louvre are for security, not tickets, and using the Carousel entrance usually means a short line. I think you can pre-buy tickets for the Orsay. Except for Versailles, the only other long line that comes to mind is for the Notre Dame tower - the pass doesn't help there either. While the view from there is iconic, there are other places that have great views, my faves are the Arc de Triomphe around sunset and Tour Montparnasse (not included in the pass) anytime when there's good visibility. On the other hand, even if you don't break even, the pass has the added value of giving you the choice to enter other sights that you might otherwise pass up, and to visit briefly, not feeling "obligated to get your money's worth."
One of my favorite things is a Seine cruise with Les Vedettes du Pont Neuf (by anytime vouchers online from home to save a few euro) just before sunset. Paris Walks are usually very good.