As I understand it you don't have to be military to fish Ft. Campbell. Check with the post game wardens for a permit to fish on post land-- their office is at the end of Lafayette Road, by the post stables, a couple of miles before you go in to Gate 10. They can give you maps and instructions for using their voice automated system for reserving areas. They do have a priority system for assigning fishing areas with a preference for active duty military, but there seem to be a lot of civilians who fish there too.
The Army has boats available on post at a very attractive price (I think a bass boat rents for about $35/day), so boating is not out of the question.
The post is 106,000 acres, but only about 15,000 of that is inside the gates of the actual post area. The rest is either artillery range impact area (definitely NOT a good place to fish!) or designated as "recreational land". They said they stock the streams and spring-fed ponds with rainbows and browns, but there are some holdovers from previous years that are actually pretty nice. They also told us that the post is one of the top places in the US for trophy deer, and hunting is also permitted. They also hunt turkey, quail, pigs and small game there too, but I'm not a hunter.
Dave