I am going to guess you are asking about Oakland, since that is the area connected to your question. If you do not have a car, and you want to be near transportation and lots of things to do, I would suggest the Temescal neighborhood.
Temescal is near Macarthur BART, and near many major bus routes, going north and south and transbay. There are alos lots of great cafes and restaurants up and down the expense level from Pizzaiola to the Mixing Bowl to a great Italian deli and a wonderful Tapas bar. A bunch of new Art gallaries have opened there, and you are even near Oakland's tiny Korea Town. You would also be close enough to Rockridge to enjoy all the shops and restaurants up there, as well as another BART station.
As you can tell, I love Temescal, and it is especially good if you do not have a car.
Piedmont Ave, Grand Ave, Lakeshore, Adams Point, Glenview, Park Blvd. These are all great neighborhoods, that have parks, great restaurants, banks, stores, specialty shops and more. If you have any other questions, please feel free to call me.
If you are looking in Oakland, one of the best neighborhoods that is close to public transportation is Rockridge. College Ave. has a variety of restaurants, shops and entertainment to choose from. On the other hand if you are looking in Berkeley, near the North Berkeley Bart station would be ideal. It is in walking distance to the Gourmet Ghetto and Northbrae area. There are also lots of shops and restaurants to choose from in these areas too.
The ones where you can get easy access to public transport, and have many local shops and restaurants. For Oakland, that are plenty of area's, depending on your lifestyle and requirements. Talk to you local agent to get more details about those options.
It really all depends where you want to live in the Bay Area. The Lake Merritt area is wondsergul if you don't have a car, as well as Albany, Ca. many areas in Berkeley are close to the BART line too. It all depends on what you want. Walnut Creek has wonderful properties close to the downtown too.