We moved here about 2 years ago and chose the Chesterfield/Midlothian area because of it's proximity to the city and the quality of schools, most notable the Cosby High school district. There area also nice neighborhoods in the Midlothian/ James River High School district of Chesterfield but you will pay quite a bit more. One of the most beautiful areas is around the Swift Creek Reservior. Woodlake would be my first choice in neighborhoods that are in your price range that include incredible amenites. See the link below. There are numerous parks throughout the neighborhood as well as fantastic events located on the waterfront pavilion throughout the year.
Woodlake Community Association Home Page
FYI-the elementary and middle schools are outstanding in the Cosby district as well, probably the best in Chesterfield aside from Bettie Weaver Elem and Midlothan Middle but check for yourself and see. Here is the best link I've found for verifying the scores of each school.
https://p1pe.doe.virginia.gov/reportcard/
Good luck!