I nearly wet myself when I returned from Japan to London after 12 years. I used to live in the center of London but there was no way that I could even afford a cardboard box in a doorway. I did a scout around for a cheap city and found Liverpool. For the prices you are looking at you could get something in the dead center in historic and rather beautiful building. Not as sunny as San Diego but the beaches are less crowded and you can get everywhere on foot as the center is so compact. ;)