Florida Southern is about equal distance from Orlando or Tampa airports. When we toured, the students said they use both, so that doubles your options for flights.
U of Tampa is also considered a beautiful school. You might look at some of the Florida state schools, like South Florida in Tamps (2 campuses), or FIU. I like Rollins the best, and I actually like Flagler a lot too. Yes, your daughter’s stats are high, but she may still find a good fit and be the top dog. Personally, I couldn’t get out of Lakeland and Florida Southern fast enough, but the campus is beautiful and if she wants a small (tiny) college town, Lakeland will work. I love Winter Park (Rollins) and St. Augustine (Flagler), didn’t care for Deland (Stetson). All schools will have shuttle service to the airports, but my daughter can always find a ride (about an hour away)
Of course this may all be for naught if hurricane Matthew takes out everything along the coast.
I think she’ll find schools in the south more religious than schools in the north, even if they aren’t affiliated with a church. My daughter is at a school which was not founded by any religion, but it has a non-denominational chapel which is run by a catholic priest and a Newman dorm. Palm Beach, as you know and already crossed off, has required chapel attendance. There are a few Catholic schools in Florida (St. Leo, Barry, Ave Maria (which is very very religious)), and several baptist or Christian schools too. Flagler is not catholic, but sort of is.