Seattle is far less homogeneous than Yakima (ie many different neighborhoods) but overall I think you will do fine. I used to be in Yakima one weekend a month (USMC reserves) and I can honestly tell you that Yakima is one of the cities that I hate the most, it just plain sucks to me. On the other hand, I absolutely love Seattle!
(now you know were I am coming from)
Crime isn't too bad in Seattle. Car break-ins are probably the worst thing, mainly because folks usually park their cars outside and they are an easy target.
You can rent a 2 bedroom place in a good area of Seattle for as low as $800 a month, although $900 is probably a lot more common (but that gets you in a really cool area like Greenlake). A $1,500/mo place is going to be in a brand-new yuppie area which you probably wouldn't want to live in anyway. There should be plenty of jobs available in the areas that you are interested in.
As another bonus, if you are single, Seattle is a great place for dating (provided that you are not a Republican

). You also can manage to not have a car and just take the bus (or have a small scooter) and that will save you quite a bit as well.
Hope that helps!