Being a Florida native it is so funny to me to sense the fear that snakes and alligators have instilled in our out of state visitors. Makes me chuckle.
Meanwhile, this Florida boy goes out of state and I'm scared to death of going off the fairway because I might not know what the local poisonous plant life is or types of spiders I might encounter. I do not like spiders. Alligators and snakes I consider a treat if I get to see them on the course and they don't scare me in the least bit.
Turkey Lake is your best option in Orlando and its the closest to "tourist town" as us locals refer to the Universal / Disney area and is the better courses in Orlando proper.
Barnett Park is 10 minutes northeast of Turkey Lake and has another 2 courses, both solid, but not mind-blowing or must play by any means. You will enjoy Turkey Lake more. Barnett Park is in a rougher low-income area known as "Crime Hills" (actually Pine Hills). I've been playing at Barnett since 2006 and never really had any problems, but you definitely might see some homeless people there. It's more of a locals course than a popular visitors course. Just finish before dark and you'll be fine if you choose to check it out. The park itself is actually very well maintained and navigation is very straight forward. On a nice day, Barnett is actually a beautiful set of courses.
if you want to play something even nicer, make the trek north up I-4 about 40 minutes and go to DeBary and play the 2 courses at River City Nature Park. The original course is one of the top courses in the state similar in caliber to Turkey Lake T2.
A brand new Gregg Hosfeld designed course was installed recently in Clermont @ Lake Hiawatha Preserve and is probably my new favorite course in Central Florida at the moment. It was barely finished in time for the recent Lake County Trailblazer tournament and is on the most beautiful property that appears made for disc golf. Considering how new it is, it plays like a well-beaten course already and at par 64, it really challenges you. Hole 16 is a par 5 hole that is probably my favorite in all of Florida at the moment. I would think its within 35 minutes of the Disney area, you just have to take the turnpike north for a few exits and then take highway 50 west a bit into Clermont. Absolutely gorgeous area. My wife and I are looking to move out that way next year, especially if Lake Hiawatha Preserve becomes officially permanent. It's T2 on steroids. Only blue tees installed at the moment so not exactly beginner friendly, although my 9yr old daughter played the whole thing and shot a 139.