Actually, we just started camping last year after completing the TD, so I have not been to a ton of Nebraska parks.
Ft. Kearny is close, we've been there, pretty nice and quiet with several small fishing ponds.
I have a friend that tells me there is nothing funner than camping on the sandy beaches of Lake McConaghey, but I haven't gotten there yet. Drop the 4X4 into Low lock to get on the beach! Harry Strunk Resevoir by Cambridge is nice with good boating, too. Lots of wildlife.
We drove through Mahoney last winter, did not stay of course, being it was wintertime, just checking it out, but there looks to be tons of activities to do there including a huge pool/aquatic park, plus the Strategic Air Command Museum and a drive-thru safari animal park is close. That would be a good one to check out.
There are many, many more, but I am kinda new to this and haven't visited alot!!