You could go to Sea Rim State Park for a few days, then up to Martin Dies S.P.. If you have the time, you could then go up to either Fairfield Lake S.P., or Fort Parker S.P.. All of these have camp sites that are right on the shoreline of a lake, so your kids could fish quite easily. Of course Sea Rim would only have surf fishing.
The nice thing about Sea Rim is that you have miles of beach to hike (kids tend to like the beach). Also, there are only about a dozen or so campsites, so once the daytrippers leave in the evening, there aren't a lot of other people around. Downside - in June at least - will be the mosquitoes, but almost anywhere you go in six hours from Houston will have them. Also be aware that the campsites have no shade, so take your own.
Martin Dies is a lot less busy than Lake Livingston or Huntsville S.P.'s, which tend to be zoos in June. There is some pretty decent fishing at Martin Dies, and wildlife to see as well. The park sits on both sides of Hwy. 190. I think the fishing is better in the unit on the north side of the Hwy, but there are more campsites adjacent to the lake in the unit south of the Hwy..
From M.D.S.P, you could go up to either Fairfield Lake or Ft. Parker S.P's., and then come back in to Houston on I45. We prefer Ft. Parker as there are a lot fewer campsites, but Fairfield has some really nice pull-throughs that were built recently, and that are right on the water. The lake at Ft. Parker is a lot smaller than Fairfield. You can go beaver hunting at Fairfield Lake too!
Please keep in mind that we have not been to these parks in June, so I cannot tell you how good or bad the crowds are. But I can say that I have never seen them as crowded as Hunsville or Lake Livingston S.P.'s. Also, I would skip Village Creek S.P.. It isn't very big, and the only fishing is from the elevated banks of the river, which isn't ideal for small kids. Brazos Bend is nice, but always full at that time of the year. Just be on the lookout for alligators there, as they can be found sunning themselves right on the hiking trails. Guadalupe River State Park has decent campsites that have decent spacing, but the area by the river will be a zoo at that time of the year. I've not ever fished there, but given how many swimmers there will be there in June, I can't see it being a good place for fishing.
C
