Totally. The one thing to be careful of is that the road over the back of Yosemite to Death Valley isn't open all year - it can be closed as late as the first week of June. If it's closed, you're going to have to take the long way 'round through Bakersfield.
3 nights in Vegas is fine, but you wouldn't want to do more than that. Yes, the traffic in LA is terrible, and all the museums are over on the other side of the city from Anaheim - driving from Disneyland to LACMA is roughly the equivalent of driving from Changi to Woodlands via Jurong. Keep that in mind when you're planning your LA travels.
What are your dates? In Vegas you'll be able to do that easily, especially midweek - midweek you might even be able to get something fancy like the Vdara for that price, on weekends you'll want to look at the Monte Carlo or the Mandalay Bay.
In SF, yeah, you're going to have trouble. Let me know your dates and I'll have a look.
I was there last week: Monday was single-digits and chilly, Thursday was nearly 20 degrees Celsius and disgustingly humid, Saturday night and Sunday morning was a full-on blizzard. (I spent an hour on Sunday morning queuing for rush tickets to School of Rock, which incidentally is brilliant, and nearly froze even though I was wearing a shirt, a sweater and a heavy jacket.)
You're gonna need to pack for winter and summer, sorry to say.
You've missed a brilliant opportunity to rack up some hotel points - you're staying across three different chains there.
Well, theme parks on the east coast: you're pretty boned, especially this time of year. Your missus will have better luck; the east coast is full of historical sites, and nature (though you won't get a lot of nature in the middle of NY and DC, aside from Central Park).
Wow, don't take thousands of dollars in cash - carrying that much cash makes you a great target for muggers. Use a credit card instead.
Siyu, that goes for you too:
Always, always use a credit card. Taking thousands of dollars of cash is just dumb.
