There are lots of apartments in that area (and getting to be more by the day--I'm looking out my window at Kirkland right now!), but to give you an answer about what's in your price range I'd have to do the same research you would. I'll just say that most of the formulas for what's an affordable rent are 30% of your gross monthly income, and I really have no idea what that is for you since you only list your net pay, and even then it's not really net because you have deducted "savings, etc" which could be just about anything.

Oh, and there isn't a train in that area, but if you pick the right neighborhood you can get good bus service.