hi--- I have lived in Miami for the past 25 years. Yes, a lot of areas are very dog friendly!! There are several dog parks and many restaurants that have outside seating allow dogs. I go to a yorkie meet up-- and I know there are other groups.
I know many condo and apartments allow dogs -- small under 20 lbs - I am not sure if you are going to buy or lease. The prices for houses/ condos are at a all time low.
There are areas that are mostly Hispanic - there is a lot of diverse culture in Miami. And the weather will be, well, very very different!
If you need more info. about dogs, places to live etc.-- I would be glad to share --pm me anytime.
What part of uk are you in? My brother was in Yorkshire several years, I visited when his son was born.