What about Salt Lake Airport? Its only 6hr drive and you could stop and see Zion. Just a thought...
If you do fly straight into Vegas, don't worry about rain....there's PLENTY to do aside from RR, climbing wise we have good limestone sport, and single pitch granite all within about an hr from city center. Jtree is only 3ish hrs away and Zion less than 3 the other way, and the other other way is the Grand Cyn/Sedona in 4.
And of course you have Las Vegas!
Ah, The King's Head in Santa Monica. Spent many an evening there with my Brit friends. Saw Richard Branson there. That said I still recommend skipping LA and go directly to Vegas. If it's raining go to JT for solid rock.