Hi, We lived in Beaufort several years while at Parris Island and are actually going to retire there. I don't know your price range, but rents within 10 miles of the bases usually run about $900-1500, averaging around $1100 depending on how fancy you want to get. It's actually cheaper to buy in a lot of decent neighborhoods. If you like more of a tranquil outdoors location, Ladys Island (about a 20 minute drive to either base) is nice, with big lots and oak trees, houses prices $120-500K or so. If you are looking closer to town, there are several neighborhoods. If you like a downtown walking area, downtown Beaufort or Port Royal is usually pretty pricey, with mostly antibellum type homes. Homes further out tend to be more Florida-style. The very closest housing is just across the street from PI Gateway with 2BR condos renting for about $1000 (waterfront) but you can also buy/rent a ranch-style brick home at Shell Point, an old neighborhood, about 5 minutes from PI and slightly further to the air station. There are lots of active duty and retired Marines in many of these neighborhoods so in generally safety is not an issue. I don't know which school districts are better/worse.
We also recently looked at some houses on Lady's Island that I am told rent for about $1000-1100 in a couple of subdivisions with 3-4BR/2BA, garage, about 1/4 acre lot and about 30% of the homes had USMC flags. The neighborhood is "Sam's Point Road" and there are houses of all sizes and prices, and a fishing dock at the end of the road. We really liked that neighborhood because of the oak trees and the water. We found homes from $120K and up, but many are for rent, too.
Hope this helps! Semper Fi, Laura