Time for a contrarian view.
I've taken San Berdoo canyon at least twice, admittedly only in the downhill direction. I don't think it (or any sight) in Joshua Tree comes close to matching Titus Canyon in Death Valley.
Incidentally, there is at least one other dirt road which accesses the park and will save you the entry fee. I have taken one from the north side of the park off of SR63, east of the town of Joshua Tree.
Joshua Tree is pleasant and you will see a lot of Joshua Trees (but strangely, not the largest Joshua Trees in the world, those are on a forest service road in the San Bernardino mountains). There's also some cholla in the lower desert.
If you have a 4wd vehicle and know how to use it, I would quite frankly chose some interesting parts of Anza-Borrego State Park over Joshua Tree anytime. Or parts of the East Mojave scenic region -- the cave tour, Kelso Dunes, Kelso, and Hole In the Wall, just for starters. For those parts of East Mojave you don't need 4wd. But to get to the pony express station or to see the genuine wagon train tracks still visible in the desert landscape, you do.
In short, Joshua Tree is OK (and as an extra bonus, the southern entrance was used for some scenes in the movie "Seven Psychos") but there are other parts of the California desert outside of Death Valley that I think are more interesting. Plus not only are they less crowded, you aren't always seeing those "benevolent dictatorship" no-no signs erected by the Park Service.