JT is great for stargazing and photography.
There are few trails. Cross country hiking is most common. The northern part of JT is higher in elevation and bitter cold and snow is not uncommon in December. The southern part is lower in elevation and warmer. There is one entrance at the south, a couple in the north end.

This is what the southern entrance area of JT looked like in Dec 2008.
Water (lack of) can be a problem.
However, I hike there a lot in winter.
Anza Borrego has lots of possibilities in December.
Regarding Desert Skyline… can become a mountaineering trip the last couple of miles if it snows and ices up. Ice axe and crampons required. Some people have difficulty navigating parts of it.
You might find something interesting in my Trip Reports page. I live in Palm Springs, but usually spend the last part of every December hiking in southern Nevada — more opportunities for longer hikes and water is generally easier to find. Enjoy yourself, whatever you choose to do.