There is such a wide variety of housing options available in Williamsburg that that is a difficult question to answer without more info.
If you are looking for a typical, new construction rental around the Bedford L, you'll find studios starting at $2200, one beds starting at $3000, and two beds starting at $4200. Three bedrooms are rare and usually converted from a two bedroom. Something like that would start around $4500.
But there are four train stops; farther = cheaper/sf. There are many different types of buildings; older = cheaper - unless it's a loft, then it could be older = more expensive. Then there are fee vs no fee apartments; fee apartments should be less expensive monthly and it should even out in the net.
I'm a real estate agent so I can give you an idea. Right now, I have a 1 bedroom in a pre-war walk-up for $1550 with fee, I have a 1 bedroom in a new construction full-service rental building for $3400 no fee, and a 1 bedroom loft in a condo building for $6500 with fee. Huge variety.
The best thing is to look on a map-based site like padmapper.com to get an idea of median rates, nearly block-by-block.
Now, as far as whether you should move to Astoria: I'm biased because I live and work in Williamsburg, but I cannot imagine living anywhere else.
Good luck!
