There is some trails in Joshua Tree NP: Old Dale Road and Brooklyn Mine Road are pretty good ones. Campgrounds in the NP and if you head out into BLM land on Old Dale there are good free open camping spots there, just no facilities or water. I was just out there in May with my Outback by myself and did not do all of Old Dale but a good portion. If it gets to tricky just turn around, nothing wrong with that.
Also the trail from Pioneer Town to Big Bear isn't to bad. I am trying to get back up there myself before the snows hit. There are several trails off Hwy 38 to Big Bear that aren't to bad. Don't know your ability though.
Finally out in Lucerne Valley is there are lot of good trials, use to race MC's out there for 38 years.
Let me know when your going and I'll try to make it. Always looking for some off road adventure.
For my Joshua Tree run see here
https://tvpjourneys.wordpress.com/2017/06/07/a-little-day-trip-to-joshua-tree-national-park/
Are you a member of the OB - West Facebook Page, might get some good leads there.
https://www.facebook.com/groups/OverlandBoundWest/?multi_permalinks=1838534046477084¬if_t=group_activity¬if_id=1503950011803214