Rank Important? UW VS BC help!!!

I am trying to decided to transfer to University of Washington in Bothell Washington or Brooklyn College in New York City for my undergrad. How important is the reputation in terms of getting a job or applying to graduate school? As of now the plan is to apply for grad school Occupational Therapy after I finish undergrad but honestly I am not certain. Here is a little background information.

I am in my mid twenties and lived in Seattle my whole life. Ive wanted to get out but stayed in state until I figured out what I was going to do to save money, and really, because I was scared. Life has and is happening and I am starting to realize that there are other aspects to it other than school.

The practical side of me says stay in Seattle for 2 more years to finish my degree, save more money and then leave. “what is a couple more years of doing the same thing?” is what I have been saying for the last 5 years. Everything else tells me to go to Brooklyn because I think I would learn more than just academics. With that being said I am not trying to run away from my hometown to become famous or think NYC will bring me fortunes. I just think that it would be a good life experience. As strange as this sounds I want to feel uncomfortable and not know anyone. Money is not a problem, actually it would be cheaper to go to nyc.

I know NOTHING about Brooklyn College other than the rankings online which are much lower than UW. That is a lot of scattered information but honestly all I want to know is, generally speaking, does the type and rank of school you go to important?

Any input would be much appreciated!