Campground or RV park?
There's a RV park at the fairgrounds (might now be called Expo Center) at the north entrance. Another at the Claremore Expo Center. Nice RV park (Cedar Oaks) on Grand Lake in Grove; one of several on the lake. There is also Mingo RV park near the intersection of I-244 and US-169, reviews are mixed because some people don't like to be around long term residents who work for a living. I have no personal experience there, as it is too close to home to be staying for the night.
For campgrounds, the state parks will have campgrounds open: Disney at the south end of Grand Lake, Bernice on the northeast side of Grand Lake, Spavinaw on Spavinaw Lake, Twin Bridges up by Wyandotte, Osage Hills in eastern Osage County between Pawhuska and Bartlesville. West of Tulsa, Lake Keystone and Walnut Creek state parks on Keystone Lake.
Most of the time I would recommend the COE parks, but for many of the properties the main campgrounds close for the winter at end of October when the volunteer hosts leave for warmer places. Some keep a small collection of sites available, will have electricity but water might be turned off until spring.
I think Woolaroc, on SR-123 south of Bartlesville, is worth a visit. It stays open year round.
I also like Tenkiller Ferry Lake, a COE on the west side, state park east of the dam, and Greenleaf Lake state park, just outside of Braggs on SR-10. That's more like east central, than northeast, all south of Muskogee, almost to I-40.
