There are currently 9 homes listed under $450K in the city, excluding District 10 (Bayview, Hunters Point, Visitacion, etc...). Most need work or are not in great areas.
If you are open to the easy bay, you will get much more bang for your buck there, especially if you are willing to buy a place that needs updating and/or can go a little higher. An excellent example: We have clients who are in contract on a 3BR 2BA 1888 sq ft house in Rockridge now for $540K.
I would consider looking near east bay BART stations if BART is a big deal for you. I would also speak with a lender to get an idea of what you can actually afford, then you can balance that against what you want to afford. If you would like some assistance figuring out what area(s) make sense and/or lender referrals, our contact info is below.
Lance King/Owner-Managing Broker