Moving to seattle for uw law

My wife and I currently live in eugene for my undergrad. Looking like uw for law school so now am doing research. We currently pay 2600 for a 3 bed 2 bath townhouse with a yard and 1 car garage. I suspect we will have to give up space and pay more but not sure what a realistic budget should be.

Ive been looking at rentals and it's seeming that near uw it's shared rentals and I'm not familiar with the area to know where to avoid or what would be close enough to work...

We need our own place...2 bedroom preferred but a larger 1 bed would work if must...

1-2 parking spots... huge plus for a garage spot but not a deal breaker

We have a dog and a cat so ideally atleast a small yard for dog to use bathroom

Close to uw law for an easy commute via bike or lightrail

What's a realistic budget to get all that and where should we look/avoid.

Any pointers for any companies or agencies that help find housing?