Having just concluded my 2nd search for a rental in the Bay area, I thought its time to put down some of what I've learned, in the hope that other folks looking for rentals will get some helpful information.
1) Commute - Decide how much time/ fuel you and your family want to spend driving each day, to narrow down the localities you could choose to live in.
2) Choosing your neighborhood - Chances are you are moving into the bay area for work, in which case of course you'll want to be close to work. Now when you look at neighborhoods - look for one you are comfortable in - downtown, suburban, up in the hills, by the highway. Speaking for myself, I was used to a busy downtown atmosphere, but thought "resort style living" would make a nice change. It didn't - was bored by the quiet stillness, and had a lot of trouble getting to public transport.
3) Set your budget - decide what figure you are comfortable paying out as rent, before you rent. You will have to do some window shopping/ research before you can do this to get used to what rent levels there are, but its time well spent - that way when you see a apartment you want you'll know right away whether the rent makes sense or not.
4) Amenities - look at the amenities that come with the apartment.Parking, Laundromat,Swimming pool, gym, jogging track, accessibility to public transportation etc. Carefully evaluate which ones are important to you, which you will use, and which are just nice to have. Then use that to evaluate the rent.
5) Monthly charges - One you have chosen your apartment look at the components of the rent careful. Deposits - are often not returned fairly, so be prepared to let go of that amount. Many apartments will send you a bill for utilities - water, garbage, drainage etc. - which is not standard, but make sure to ask how much that would be per month and add it on to the rent for comparison with other places.
6) Pets - if you have a pet the good news is that many apartments welcome pets. Most charge an additional pet deposit, which is standard, and some charge a pet rent - which is not.
7) Older Buildings -Most apartment buildings are old - so you will get lead paint, termite, bed bug warning notices. Specifically avoidable are apartments with mold and those on higher floors specially if you have kids. The walls and floors are really thin and all sounds and many movements carry, so just be aware of that.
8) Look em up - check out the rental reviews on line- yelp, city data forum etc. Most of the reviews are cribby, but at least you'll get an idea of what they are commonly cribbing about and then you can decide if that is something you can live with or not. For example "noisy kids" is common, but if you have kids too...why not :)
9) Bargain - while most property managers will pretend to be busy and ultra efficient, if you really want a place, make sure to discuss the pricing and amenities and chances are you'll get offered a better deal.
10) Be ready to sign up right away, the rental property market here is fast, and when you like one, be ready, checkbook and all to commit so that you don't lose the chosen one.