If you paddle from Madison, you can only do so upriver if you want to come back the same way. Going downriver you'll encounter some rapids and rocks and you'll have to keep going. Plan a trip, bring your own kayaks (the park does not rent anything), put in at Madison and take out at Suwannee River State Park (make sure to shuttle vehicles so you have a ride back to Madison). They don't allow overnight vehicles at Madison.
I'm not certain about the rivers. It has changed so much to accommodate more visitors so it is best to call for rental information. We brought our own rafts, etc to float on the lazy river. I hope this info helps.
During the summer season you can rent tubes at Madison Blue Springs.
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