Search for condos for rent in Hampton, SC on Apartments.com. With 0 available, you can find the right condo with the floor plan and amenities that fit your needs. Many condo rentals are pet friendly to fit renters' lifestyles. When you rent a condo, you’ll likely rent from an individual owner rather than a property management company. This means units in the same building may have different features and layouts. Be sure to check out the photos and take a tour of the unit as you search for your Hampton home.