Ok, being from Texas originally I have to say I HATE Houston. It's my least favorite city in TX. (Sorry all Houston lovers - no offense meant - my brother still live there and loves it ... but it's not for me.) It's humid and flat and has cockroaches the size of small cats.

(Only partially joking about that last.)
Portland, OR is not quite as big as Seattle - a lot like San Francisco w/out the earthquakes.
Austin, TX is where I went to school and it's gorgeous Hill Country. There's a big lake nearby. I'd move back there if I had to live in Texas again.
Charlotte, NC is a fantastic city - clean and not too big, but not too small, lots of art and culture. My biggest problem with Charlotte is that most of NC is fairly religious (it's the home of Billy Graham) and so a lot of local laws are religious based (blue laws about what you can sell on Sundays, a lot of places not open on Sundays, etc.). North Carolina is also a big tobacco producing state, so the smoking laws are MUCH less stringent that what you're used to in CA. It will be a huge culture shock.
Albuquerque, NM - another gorgeous city, if you can see the beauty in the desert. Not so much close to water, but the mountains are gorgeous and you're a short drive from Santa Fe and Taos and so many beautiful places. It's a growing economy and great cost of living. And very laid back and charming. I love, love, love NM.
St Louis, MO is a wonderful town - right on a the river. A little hot and humid in the summer, but great culture, great museums, a good hospital system, and a really good cost of living.
Cincinnati, OH is another just like St. Louis w/out as much humidity. I'd move to Cinci in another heartbeat. (But Portland first, since I'm really a west coast girl at heart).
Ok, having said I hate Houston for humidity, flat, and roaches - if I could move anywhere for at lesat a few years I would move to New Orleans. Yeah it has problems. Yeah it's humid and miserable in the summer. And yeah, their roaches could win in a throwdown with Houston roaches ...

BUT. New Orleans is a city amazingly rich in culture and history (which fits your requiements) and right now they NEED medical personnel and they need people to move *to* the city and help with the rebuilding and growth. There are also several well known colleges and universities in the city. Even if you moved there for a fixed length of time - say 5 years - I think your life would never be the same after. It's the city of my heart and I have thought many times about moving back except that I already have an established business where I am.
Those are my suggestions ...