You should be able to walk around most of Andorra la Vella. The town is really in two parts. There is the newer section at the North end of the town that is very commerical with lots of shops. The other half is the older half, down across the river and to the South and West. This also has quite a number of shops and places to eat and also the historic part.
If you stay in either of these areas, you can easily cover on foot, but walking from the end of one half to the other will take a good half hour or more, so it is worth taking the local bus which is cheap. Be sure to read the timetable and routes carefully on the bus stop.