I think this is where you're going to run into a bit of trouble. LA -> Vegas -> Page -> Grand Canyon Village -> Vegas is a lot of driving! It's basically (give or take a couple hours) like driving from Singapore to Bangkok.
I'd do less time in LA (it's not that great, really), maybe one extra day in Vegas, and chop out Page (where Antelope Canyon is). That way you'll still see a bunch of great things, but you'll be doing a lot less driving and you'll be able to enjoy it a lot more.
Whenever someone asks this question, I always ask "what's your dates, and what's your budget?". Hotel prices in SF and Vegas especially will swing around wildly based on whether there's a convention in town hoovering up all the hotel rooms; and people have different tastes! I don't know whether you're a Holiday Inn Express kind of person or a St. Regis person.
For your dates in Vegas, at least, you're in luck because they're stupidly cheap right now. I can get the Mandalay Bay for April 12-14 for sixty bucks a night, which is just hilariously cheap; if you want to be closer to the middle of the strip, and/or you're a Starriott loyalist, the Cosmopolitan is $140/night for those dates. (Pro tip: the Cosmo is the right choice. Try breakfast at Eggslut, but get there early.)
That's going to go against your rooms in San Francisco, though. For April 4-7 there must be a something on in town, because my usual cheapo go-to, the Park Central, is nearly four hundred bucks a night. Even the janky-ass Holiday Inn out on Van Ness is four hundred a night, you'll need to go all the way out to the airport hotels to get anything reasonable under two hundred bucks a night.