Northern California. Or Oregon.

If biking is your primary concern, this is not where I would move to. But there is good riding to be found just about anywhere.

Is your profession such that you can go pretty much any where?

Club riding? Racing? Centuries? Cruising the back roads? Social cycling events? All can be had here or most places in the southeast, to greater or lesser degrees. Knoxville and Chattanooga both have active cycling communities and great places to ride. If you want less weather, go farther south.