Do I need a car to tour Brugge and the surrounding area? Would like to see the WWI exhibits in countryside and some small towns.
For Brugge, no, a car would be more of a hastle than a benefit. The historical center is not very large, and easily explorable on foot.
If for WWI exhibits, you mean the Ypres Salient, yes, a car would be very useful. There are also bus tours available.
For other small towns, Belgium has an extensive bus system, but it can be hard to figure out sometimes.