You could look at Lawrence, Kansas.
It kinda sorta meets your criteria.
Low cost of living - Definitely. Not the lowest of the low, you'd have to go elsewhere in Kansas for that, but still pretty good.
Mild Climate - Sort of. Mild Winters. Mild Spring and Fall. OMG SWELTERING SUMMER. June through August, you're looking at 90F+ and during the hottest weeks, over 100F. A lot of humidity too. But when the weather is good - lots of bike trails, lots of outdoor events, a lake or two pretty close by, great Farmer's Market, really nice downtown area.
Socially liberal - Well, Lawrence itself is really liberal. There are three counties that always go blue - and Lawrence is in one of them. But the rest of Kansas - there's some crazy right wingers around. I hesitate to call them Republicans, even, because they're on the far right of the crazy scale. Really socially conservative. That's frustrating for a lot of Lawrencians, but overall the social conservativism doesn't really bleed into the city. So, for example, while our state legislature would be happy to pass a law saying you can have an anti-gay sign posted, you would never actually see that in Lawrence.
It's about 50 minutes to the nearest international airport (in Kansas City), and of course all the other stuff Kansas City has to offer for day trips, etc. If you want to lean toward a larger city, Kansas City actually has a fair amount going for it. More fiscally conservative, but without a ton of crazy.