At that budget, you can get a nice place in scripps ranch or carmel valley, live the classic american family suburban lifestyle, have quality schools, and be 20 minutes from downtown outside of rush hour. But not lots on the “culture” end of things.
But really you have a million options depending on what you prefer. You could get a very nicely restored/renovated place in some of the very central neighborhoods (Kensington/Normal Heights/University Heights) and be able to walk to restaurants/stores. You could get a condo in downtown itself. You could get a place with some land out in the La Mesa/Mt. Helix area. You could probably get a newer 5000 sq. ft. Mcmansion in Chula Vista for that price (20 min. from downtown w/o traffic or speed limits).
You just need to decide what’s most important to you.
