As mentioned, Maryhill is nice. The museum there is neat to see also.
If you want to go a bit farther east, Crow Butte is nice too. It's on an island with some hiking trails, some wineries nearby, and a major destination for water sports.
Columbia Hills State park across the river from The Dalles is small but pretty nice also.
On the Oregon side: Ainsworth, Memaloose, and Deschutes River State Rec Area are ones we like.
Fair warning: almost any of these will have trains running adjacent to it (Crow Butte they're across the bay, maybe 1/2 mile away) and the Oregon side ones will all be near the freeway.
