If you rule out every neighborhood in Boston based on what happened twenty years ago, you won't find very many places to live . The seaport area/South Boston has many stories as does Chelsea, Mission Hill, etc., but time marches on and things get better.

I wouldn't rule out South Boston if you can find the right place. There are so many beautiful victorians and condos with water views and fairly easy access to supermarkets, drugstores. You should be able to get deeded parking with your budget. L Street to Castle Island is full of beautiful places. The seaport area is nice but you need a car to get anywhere if you need to run errands. I would still consider Admiral's Hill even if you just go over and take a look at it. As for Belmont to the Financial District in half an hour, I'm not so sure. I've done that trip and one traffic problem will turn it into a one hour trip. You could take the train from Belmont to North Station and walk though. One other thought - have you considered Charlestown? That is easy access to the financial district and Monument Square is beautiful.