I have a come across the 'vegas.com' webste. Is that the cheapest one to use to book a place? Has anyone been to vegas and perhaps might recommend their hotel?
There are all sorts of offers available online for different hotels and casinos. It depends on what you can find/what is available as to where will be the cheapest place to get the accomodation (at that time of the year you may not have a huge choice of offers).
Have a look at that website, then check a couple of others and try going direct to the hotel/casino website. You'll have a rough idea of what you should be paying and you'll know if your getting a good deal.
The hotels and casinos are all very good. Any of the big names will be excellent. If your budget can take in a night or two at the Bellagio then it really is a must do! The place is absolutly amazing and worth the extra few $'s for the experience. Given the time of year you may not even be able to get a room there though.
Stick on the strip (really is worth it. It just ain't Vegas if you're not on the strip and with the heat over there walking from a hotel off the strip is out of the question. Lots of taxi's, but so much easier to stay on it) and go with a well known name. Some are nicer than others but not massive differences to be honest (though I only know the rooms from the Luxor [good, not great, elevators (inclinators, they go at an angle) will have you a little queezy but is a good spot] and the Bellagio [wow! can't wait to go back - kinda makes the others seem also rans!]).
One or two are getting a little old and not as attractive as the others but the standard in general is very high in the city.
I am being advised not to bother staying in LA a night to recover but head straight to vegas. Would anyone agree?
Personally, if I were going, yes. I would agree. I loved Vegas and can't wait to return. Whether it's the right decision for you? Depends on how tired you'll feel after the flight, how well you can sleep on planes, how excited you feel about it (the buzz will keep you going - not to mention the artificial conditions within the casinos (pumped oxegen etc.) which mean you never feel as tired as you should).
I've never stayed in LA, but some find it a little rough round the edges and a completely different atmosphere to that of Vegas (I believe one quote was "Taxis door to door wherever we were going in LA, I just couldn't walk there!"). May take you the night just to get out of the airport there, it's huge. If you don't plan on going to do the West Coast thing again (LA, San Fran, San Diego) it may be worth giving it a night, but personally I think Vegas is a different holiday and shouldn't try and squeeze too much in.
(Up by the giant Coke Bottle [you'll know what I mean if you look up a pic of the strip or when you get there] you can pick up tickets [at half price] for all the tour type stuff [Helicoptor tour of the Grand Canyon, show tickets etc.])