Indian Cave, south of Nebraska City, and Ponca, northwest of Sioux City. No fishing at either unless you can fish the Missouri River.
Summit Lake, west of Tekamah, has camping and many people fish the lake.
Whiterock Conservancy, south of Coon Rapids, Iowa. Campsites surrounding the Starfield Campground are back in the trees. No fishing at all.
Smaller campgrounds and fishing at Czechland Lake, north of Prague, Homestead Lake, west of Prague, and Timber Point Lake, southeast of Brainard.
Our reason for going to these places is to get away from city lights for astronomy. We don't fish. We used to tent camp but now we sack out on a mattress in our van for a few hours so that we don't fall asleep on the way home after a late night observing. Before going, I recommend you look at them with Google Maps in satellite view.