1- Most liberal on west coast would be St. Pete, Tampa (in the city) and apparently from reading here, Ft. Myers. Definitely NOT Naples and Sarasota, which tend to be upper-income and very red.
2- Most liberal on east coast are Miami, Ft. Lauderdale, West Palm Beach. Definitely NOT Jacksonville and Daytona Beach.
3- If you want to avoid almost all cold weather, think south Florida or the Keys. Even here in Orlando, we get maybe a week of cold weather. Sometimes less.
4- Your choice will also depend on how politically active you wish to be and how much you want to vocalize your beliefs. Even here in the Orlando area, there are many conservatives.
5- As someone said above, east coast tends to have better waves and surf, but the gulf water tends to be warmer.
6- Another factor to consider is bigger city (more to do) versus small town quiet. You might want to take a look at the Florida Keys (almost always warm), but it's small town all the way, except for Key West. However, if you love water-related activities and fishing, it can't be beat, really.
I love the Orlando area, but I'm willing to admit it's not for everyone. Traffic tends to be pretty heavy, especially at rush hour. I'm also pretty good at keeping my opinions to myself, which helps me cope with the conservatives here.
You have a lot to choose from and a lot to consider. I also like Shenmue's area (Pasco County) and even Spring Hill (Hernando County) to the north of her.
Best wishes and ask questions if you have them. 
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