I won't pretend that I can give a lot of information on this particular site, as I didn't visit it and I can't seem to find anything on the internet with information about its collection. It was closed when I arrived, despite the schedule saying that it was open. Nevertheless, I would imagine that this particular exhibition space continues primarily examples of local artists who would be classified as contemporary, and the space is fairly small, as too the collection is likely small. There is an interesting small statue outside - I can't really tell if its supposed to be a rocket or just some sort of toothless comb.
The Town Hall or Mairie of Bourg-Madame is not a tourist attraction, but it does provide for a fairly large part of the town and is probably the most noticeable attraction in the entire village. It is just across from the Rue de la Gare, so if you come here by train you will undoubtedly see it. There is nothing Catalan or Pyrenean about the building - it looks like any Mairie in a French village. There is also a smalll park next door, and a small fountain as well.
The statement that Bourg-Madame is devoid of historical interest is not at all true. The Saint-Martin d'Hix church, on the Rue de l'Église, is in fact quite old, dating from the 12th century. It played an important role in the religious and political life of the Cerdagne, being a place where the counts would occasionally meet. Unfortunately, the original Christ, dating from the 13th century and in traditional Catalan style, was removed and put in the national Catalan Museum of Art. Still, there are a number of other interesting Mediaeval paintings inside the church. The problem is, of course, that the Church is only open at specific times, posted on the doors, and is not generally open for tourist visits. Still, you can always just enjoy the Romanesque architecture of this building, which seems lost among the modern developments of the town.
If you want to walk from PUIGCERDÀ to BOURG-MADAME, you have to go through some ugly new developments. Its not the best trip, nor is it easy (there is a lot of hiking up and down steep roads) but its a fairly simple route thanks to the street signs.