There was (is?) a city park with about 5 spaces of RV parking in Mitchell, OR not to far from Painted Hills. Had 30 amp electric and two water risers. Don't see it listed now. Was there in 2016. Clyde Holliday St Park might be your best bet but about 70 miles to Painted Hills. Last year I checked out a few others in the general area that sounded good but plans changed.
Wallowa St Park is really nice. No cell reception in the park as of 2016. We stayed at Wallowa River RV Park, a small mom and pop operation. Nice guy, laid back. River on on side of property if you like to drown worms. Shorter drive through sites.
Sisters Creekside in Sisters, OR nice park. Kinda close quarters but nice. Walking distance into town and restaurants. Tumalo St Park is another one near by.
Mtn. View RV in Baker, OR is a nice place. Well maintained, friendly staff.
Decent fuel stop in Redmond is a Fred Meyer Fuel. Good in/out.
I thought I saw that the Oregon Trail Interpretative Center was closed this year for repairs so you might check the website.
EDIT: Looks like the city park in Mitchell is open.
https://www.mitchelloregon.us/stay