I live just south of Lake Union (2200 Westlake building). There are several condos around that have some rentals available. They'll be a much higher quality building than an apartment of similar price.

If you want more of a social thing, then an apartment may be better. There's a building that's pretty popular called Rollin Street Flats that has a good scene.

Stuff's expensive around here, especially with Amazon moving in. Unfortunately you're not going to find a great place for under $2k.

Belltown is also pretty close and has good night life. Easy bicycling distance. There's a relatively decent complex called 2900 on First that should be in your price range.

Craigslist is a good place to look if you decide to go the condo rental route.

Good luck, and welcome to Seattle!

Thanks for your helpful advice, mate. If am not really into night life so living right in Seattle wouldn't be my priority. It sounds like Belltown is a decent neighborhood based on your description.

Belltown actually is kinda sketchy at night these days. South Lake Union has a much safer, 'yuppie' feel to it. For something a bit quieter you might consider east of the lake. There are also some nice neighborhoods (not sure of prices) closer to the university that would still be a nice short commute.