A big majority of the students at FSU are from South Florida. South Florida is definitely not the “south”. The top four counties in Florida that send students to FSU are Leon (where FSU is located) , Broward (Ft. Lauderdale), Palm Beach (West Palm) and Miami-Dade. Tallahassee is located in the panhandle but is nothing like the rest of the area. It’s progressive and liberal, always goes blue. This is the only place in North Florida I would live. There are white, Asian, black, Hispanic, middle eastern students - you name it I’ve seen them. (Live in Tallahassee and have/had children that attend FSU.). Being Jewish and from the North will cause no difficulties at all for your daughter.
As for the weather, yes it is definitely warmer than up north but it is not the tropical Florida weather that many people envision. It does on occasion get below freezing in the winter.
(I don’t know where ucbalumnus gets his/her info but about 26% of the student body at FSU is black, whereas the state population is about 16%. Yes FAMU, the other university in Tallahassee is mostly all black but then it’s an HCBU so that is kind of expected. FSU is no more of “an uncomfortable reminder of southern history” than anywhere else.)