At Poplar Tree Lake in Meeman-Shelby Forest State Park, you can explore 125 acres of flat water by kayak, canoe or SUP. There's a small daily launch fee (just $2 to $3), which is a small price to pay for a clean, safe area that's well-patrolled by park rangers.
Poplar Tree Lake is excellent for less-experienced paddlers. There are plenty of coves to paddle into, without ever straying far from the main waters. And you won't have to worry about wake from powerboats; fishing is allowed, but only in electric-motor boats.