Barolo is a small town in Piedmont. It is world famous for the red wines made there from the nebbiolo grape.
From Alba, take SP3 south to Barolo. It is 15 km from Alba to Barolo.
There is a free car park on the left as you enter the town. You can park there and get to any of the sights in Barolo in a few minutes on foot. The streets are quite narrow, so parking in the car park is a good idea.
Barolo is walkable. You can walk the entire town in 30 minutes.
Barolo is a world famous wine city. It is the namesake city for the "king of wines and the wine of kings." Barolo is a very scenic small town. The surrounding countryside is spectacular. There are some very panoramic views from the Castello. However, if you are not interested in wine, there is not much to see or do in Barolo. For the non-wine lover, it is probably not worth the drive up from Alba.
Taste wine. Taste more wine. Buy wine. There are several good wine shops in town, and a number of famous producers have tasting rooms in the town. The owners of wine shops typically have bottles open for tasting, and may open a bottle for tasting on request.
There in an enoteca in the basement of the Castello, the Enoteca Regionale del Barolo. You can't miss the Castello - it's the castle at the top of the hill. This enoteca has a lot of local wines from recent vintages. The opening hours are irregular, so you should check in advance before going there to taste. The phone number can be found on the city link below. The other shopping in Barolo is limited to small shops. This is not a shopping town, it's a wine town.
By all means. There are a couple of small bars in town, but wine is the main attraction.
Visit nearby wine towns:
Do some hiking in the surrounding countryside. 
There is a web page (in English) for the community. There are a lot of great links to wine producers, hotels and restaurants on this page.