Much like San Francisco, all of Seattle is changing. It would be a challenge to find a neighborhood that doesn't have at least some development in process, if not quite a bit. In my opinion, Capitol Hill (directly east of downtown) has seen the most dramatic change over the past 10 years - it has been thoroughly gentrified. There are a ton of jobs here thanks to Amazon, Starbucks, Boeing, Microsoft, Google, Adobe, and the like, so it's hard to imagine a slow-down will occur anytime soon.
Speaking directly to your question - and my assumption here is that you're looking for housing options - you will find the most new residential buildings going up in South Lake Union, Lower Queen Anne, Fremont, Wallingford, U District, Eastlake, and West Seattle. I'm sure there are plenty available in Capitol Hill as well.