PNW seems to be great, but I haven't spent a ton of time there.
From my experience:
Reno/Tahoe/Sac is actually very good for year-round kayaking....it would be amongst my top 3 choices for sure. The Reno WW park usually has year round water to paddle, and the creeking in Cali is, in my humble opinion, the best in the world.
On the east coast, the Washington DC area is excellent: the potomac runs year round with class 1 - 5 just outside the city at Great Falls, and good playboating....you're also 3-5 hours' drive from hundreds or thousands of other great runs in WV, PA, MD, and VA.
Asheville is great if you like to creek.
Columbus, GA would be great if you like to play.
Fayetteville, WV is pretty freakin awesome as well....with a playboat, creekboat, and squirt boat, you could paddle something world class for one of those disciplines 300 days a year.
All of those areas might have a winter where a cold snap makes you not want to kayak for a month or so (except Columbus). But they're all great
Hope that helps!!!