Having grown up with toll roads, I don't have any problem with them, especially if they save me time and traffic. And now with gas prices so high, any shortcut that sames time and distance will also save on expensive gas; I don't know if the trade-off between gas and tolls is worth it, so each person will need to do that calculation him/herself. We bought a SunPass for Florida toll roads (in addition to our EZ Pass for the Northeast) just so we would not have to stop at any toll booths and just have it taken care of electronically; I'm still paying the money but I just don't need to stop in order to do it.
But if you are determined to avoid having to pay tolls, I would suggest getting off I-75 just before the Florida Turnpike, on FL-44 toward Leesburg. Then FL-44 east to US-27 South. US-27 takes you right to US-192 which you can follow until you get near your favorite Disney destination. Yahoo! estimates the toll-free route would be ~40 minutes longer (~8% longer), without lights and traffic. In terms of distance, tho, it looks like it's only about 2 miles longer! So it looks like it would be do-able from Atlanta; you'll just need to take some smaller roads for a bit and see something of the countryside.
Good luck!