Hopefully some locals will chime in, but here are some thoughts-
Moe’s- February and March good, April might be too hot. Don’t sleep in your van at the parking, get directions from locals about where to camp.
Joes- March might be ok depending on weather. New Joes and Triassic are warmer. May is starting to get hot.
Bishop- February should be ok. I’m not sure when it gets too hot.
Other spots to consider-
Red Rocks- good winter area. Camping is mediocre. If the season is rainy you can be skunked.
Tahoe- lots of good boulders, but kind of hard to navigate as a visitor. Climbable all summer though.
Little Cottonwood Canyon- fairly close to Joes, granite blocs. Warm but climbable later than Joes.
Ibex - otherworldly spot in the middle of nowhere on the route between bishop and Joes. Quartzite boulders, pretty fun but really isolated. Wintertime
Hueco is good in February to March but there are significant logistical challenges
DM if you want any more info
Have a great trip!