Late Nov/early Dec. is a great time to visit London. If you can add even a few more days, I would try to do so. But even a short trip is good. Windsor is a great half to 3/4 day trip and easy to do by train on your own. Just catch the train to Slough at Paddington Station and change for the Windor train at Slough. Total train ride is about 25 min. Trains run regularly (every 1/2 hour or so) in both directions. Windsor is very walkable. You can tour the castle and grounds, or just view it from outside. We liked to visit Windsor on days when we'd be going to the theatre in the evening. We'd just head back in the afternoon, rest a bit and shower and change before heading out for an early supper and the show. If you are only gong to have the short time, I'd not really plan on any other day trips, but Bath is also doable on your own by train, if you feel you must. I agree that the tour company versions of the Windsor, Bath, Stonehenge trip is not worth the time or money (at any time of year, really).
I know you say you aren't really interested in shopping, but we found we'd often find good Christmas presents at some of the markets. Lots of good craftspeople with wonderful, unique, handmade items.
On one morning (I'd aim for Friday) head to the Tower of London so that you can be in line before opening. After entering, head straight for the Crown Jewels, then do the Yeoman Warder Tour. After that you can just wander around and enjoy views (good view of Tower Bridge, especially if a tall ship comes through while you are watching), and the gift shop is excellent.
If you get to add a few days, I'd visit Kew Gardens. Even in winter they have excellent exhibits, and it certainly isn't crowded. And again- EXCELLENT gift shop (a few times, we went and asked for admittance to just the gift shop - they let you go in for a short time, no charge),
Canterbury and Dover are also doable by train as day trips (even combined) on your own, as are Stratford-upon-Avon, Winchester, and even York or Cardiff (they do require longer train rides, but fun).