Lake City has a number of good hotel choices. We stayed in the Lake City Hampton Inn last July and it was a very nice, comfortable location (the complimentary continental breakfast was also good). Hampton Inn may be slightly more expensive than other roadside motels, but I've yet to see a Hampton in anything but excellent condition - and I can't say that about any other chain.
Valdosta, GA. also has many choices, and would be only slightly over the half-way point north of Lake Park.
Wherever you stop, I'd make reservations prior to arrival (by early afternoon the day of). When we checked into the Lake City Hampton Inn, we walked past a line of people going from motel to motel looking for a room, only to find "no vacancy" signs taped to locked doors. We had reservations, and the last room at the inn! The desk clerk said this was common.