The "pretty nice cabin" part will be the rub in most places. There are some great lake houses for rent around Possum Kingdom and Cedar Creek probably also Texoma. The nice ones on the water are probably $600-$1,000 per night. Turner Falls is probably worth checking out but I don't know much about rentals around there.
Despite everything I said, renting one of those houses in Broken Bow for a long weekend will probably be exactly what you are looking for if the goal is just kicking around in the woods and letting the kids throw rocks at each other while having the possibility of getting poison ivy. 😳
The first time went our kids were younger and that's about all we did (mess around in the woods, find poison ivy and have smores, etc.) and it was OK. We did do a canoe float trip that seems like it was alright now that I think about it.
Our more recent trip was the one that was kind of a dud as the now older kids wanted to "do something" and there really wasn't much to offer.