Alba is a very nice town, small and intimate. The main point to go is to eat and drink the best food/wine in Italy. Around the center there are many typical restaurants were eating and drinking is simply wonderful.
Also walking through the town is a nice experience. You can see the cathidral and the dome, sovrasting Alba.
If you have time and the sun is shining, I recommend a little trip on the country around Alba. The view is amazing and between the hills you can spot often secret places of great interest