Where can we buy a home, half an hour to an hour outside of Houston, for 325K or less?

Hey,
My husband (French) and I (American – originally from rural Central NY) are relocating to the greater Houston are from France (where we currently live). We are looking to buy a home in the greater Houston area in a town that is family-friendly and so where we can raise our son (currently 2 years old). What small towns and/or suburbs can you recommend for buying a home with a max budget of 325k or less? Are there still bidding wars for houses going on in the greater Houston area? Ideally, we are looking for a smaller home (about 1,300 square feet) on a small lot BUT that has been well maintained (is move in ready). Thank you for all of your help!