Moving to Seattle

So... it looks like will be moving to Seattle after I graduate in May to attend grad school at UW. Having never been to Seattle (yet), where do you suggest that I live location wise? I would like to live close to the university (within walking distance if possible) where the rent on apartments is not too high. I'm sure I will have plenty more questions about Seattle and the outdoor world there but I have to find a place to live first haha. Any kind of advice is more than welcome.