I did a 3 month US trip, same area (in/out of LA), same time of year (mar-may) quite a few years back. I didn't have a car so bummed rides with climbers when I could and hitched/public transport when I couldn't - a car would give you more flexibility for sure. As a result I spent lengthy periods at each spot as opposed to hopping round a lot, which, as the Dr prescribes, I think is a good thing.
Here's where I went:
1. J-Tree (easy day from LA, I caught buses then hitched into the campsite in a day) - nice scene there and really cool landscape
2. Red Rocks - I found the sport climbing a bit meh, but the long trad routes in the canyons are awesome
3. Bishop (buttermilks, owens river gorge) - the sport climbing in the gorge is great, and the bouldering is good too if that's your thing
4. Yosemite - had around 6 weeks here from apr to may. Was cold and even snowed early on, but the bonus is no crowds. By the end of the stay it was just starting to get busy. Tuolumne was still closed due to snow.
I was pretty happy with this itinerary. If I had more time I would have gone to Indian Creek / Zion as well. There's so much stuff in that part of the world that it really does depend on what sort of stuff you want to climb - pick a destination or two that are "must haves" (for me it was Yosemite) and work your itinerary around that.
Lake Louise (and Canada crags in general) are likely to be still pretty cold/snowy that time of year (maybe some late season ice climbing though?).