Things to do in Andorra:
You can try some of the spas in the area of Andorra la Vella and then in the evening follow the local crowds up to the views of the Placa del Poble.
There are great hikes to be had anywhere here but try Llorts for some obvious trails.
The mountain biking is exhilarating at La Massana.

The wintersports resorts Soldieu - El Tartar, Pas De La Casa, and Arinsal are what place Andorra on the map.
The ski area is known as La Grandvalira is the largest skiing area in the Pyrenees. If you are looking for Apres ski then be careful its not so lively but Soldieu is pretty good. Don't believe that its as cheap as it used to be but its pretty good when compared to the other eurozone rip offs.