Joshua tree north entrance (Joshua tree City) versus the South Entrance ( (Coachella City)! What is the best scenic drive?
I would definitely enter (or exit) from the West Entrance at Joshua Tree. And you could easily exit (or enter) from the north or south, depending on where you are going (or coming from).
I just checked the NPS website-- "Intermittent Closure of Cottonwood Springs Ramp off I-10". So maybe enter from the west entrance (Joshua Tree) and exit from the north (29 Palms).
In general, you can drive all the roads in Joshua Tree National Park regardless of which entrance you use to enter. It makes some difference where you want to go next after Joshua Tree National Park for optimal route.