Here are two state park campgrounds I can recommend.
1. Valley of the Rogue State Park - https://oregonstateparks.org/index.c...Page&parkId=76
Stayed here back in February on our way home from Death Valley National Park. Very nice park, close to the freeway, so convenient for a single overnight when traveling through on I-5 near Grants Pass. Reservations are accepted, but we got in just fine without one (possibly because of the time of year).
2. Hilgard Junction State Park - https://oregonstateparks.org/index.c...Page&parkId=13
Stayed here just last weekend on our way home from Moab, UT. Another very nice park that is close to the freeway, just off I-84 near La Grande. First come, first served, and is a pretty small park, so I'm not sure how much it would fill up on a holiday weekend, but it was less than 1/4 full last weekend.