My hometown. It all depends what you are looking for. The KOA, Deer Ridge, Grandpa's Farm are all decent private campgrounds. Grandpas farm is on a busy state rd and can be noisy. Natural Springs Resort just across the state line in New Paris Ohio (Richmond is on the IN/OH border)is also a good choice.
Just 20 minutes south of town is Whitewater State Park. Very nice park but only has 30 amp hookups, no water, no sewer but does have 2 dump stations and water fill station is available. The rest of the Brookville Lake area which Whitewater is part of is 10 minutes further south consists of Mounds Recreation area which has some full hook ups and Quakertown SRA that is very nice with hookups similar to Whitewater.
Richmond/Centerville does have many many nice antique shops. If you are more specific with your hookup needs and other interests I will do my best to point you in the right direction.