LOL, since this thread is older than my participation, I didn't respond or read it till now Colo. Sorry to see you have had so little input.
Yes, someone has been to Basel. I have been many times (I used to be married to a 'Baslerin'. Nuff said about that). However, that also means I did not stay in hotels when there but in a family home. So that's another reason I didn't respond, I don't have any experience with hotels there. I do like the city though and have been there during Xmas a couple of times.
Basel has a good Xmas market as does nearby Strasbourg which you could easily day trip to from Basel if you have the time. I would say it would definitely be a shame to miss Strasbourg if you are in to Xmas markets. It is the oldest Xmas market in Europe. With both Basel and Strasbourg, most of what interests first time visitors is found within walking distance of the main square. Obviously, it is not difficult to Google for the main attractions in both, so I don't see any need to list places of interest to me that may or may not be of interest to you.
One though on the Xmas market aspect however. A big part of that is the lights which means being there at night. You might even want to consider spending a night in Strasbourg because of that. A hotel within walking distance of the Cathedral would be best. I do have a personal suggestion for a hotel I have stayed in there.
http://www.hotel-cathedrale.fr/home/ Quite possibly the best location in the city.
In keeping with our shared penchant for stories though Colo, here's one about Basel. On a visit in 1991, I became interested in a Swiss artist named Jean Tinguely after seeing his mechanical sculptural creations in the Tinguely Fountain in Basel. So I visited places in Basel associated with him. One of those was a gallery that sold his works. I couldn't afford any of them but I could afford a t-shirt with one shown on it. So I bought a t-shirt.
That evening, my Brother-in-law admired my new t-shirt and so the next morning, I went back to buy a second t-shirt to give him as a present. Well, unbeknownst to me, Tinguely had died the previous evening. When I got to the gallery, the door was open but the lights were off and when I went in the gallery owner and his assistant were busy removing all price tags from all the Tinguely items. Getting the picture Colo?
I approached the owner and explained that I wanted to buy another t-shirt for my Brother-in-law. The owner told me that Tinguely had died the previous evening and they were not really open, they planned to be closed for the day, 'out of respect'. I said I could 'see' the indication of their 'respect' but as I was a visitor to the city and would be leaving, I hoped he would agree to letting my buy another t-shirt. He agreed with ill grace and I got the t-shirt.
It always remember that and how quickly after an artist dies, prices for their work increases dramatically. I have no doubt that even the t-shirt prices went up several hundred percent when the gallery re-opened the next day. So much for 'respect'. It's all about the money.