In the three times I have driven from California to Nevada (from LA, San Francisco and Fresno) I have never once had to pay a drop fee which is what is normally charged when you drive a car one way only. The thing with California and Nevada is that so many people are making that journey (i.e. LA - Vegas) that it is never a problem getting a hire car back to its original destination.

The first two times was with Dollar, booked with a package from Virgin Holidays and the third time was booked directly with Hertz. I would suggest pricing up with http://www.dollar.co.uk direct first and seeing what the cost is and whether there is any drop fee involved. Definitely shop around, although I've always found Dollar to be pretty cheap and with new cars mainly.

Are you intending on keeping the car in Vegas? I only ask, because if not, it will be more worthwhile seeing if there is a branch of the car hire company you book with in the actual hotel you are staying in. I know Dollar have desks in the Luxor, NYNY and MGM amongst others. We've never kept the car after driving from California, and just dumped(!) it in the self park garage and given the keys in at the desk in the hotel. Very simple process.
If of course you are keeping the car, then dropping off at the airport is a doddle also.

we did exactly the same (pick up LA, drop off Vegas) and found the best price with carhire3000.com...they will advise you that there may be 1-way fees when you book and they will let you know (you still have the right to cancel if the 1-way fees are unacceptable)...in our case they did (original booking was with dollar) but gave us the option to pay £12 more to avoid a significant one-way drop fee...in the end the booking was switched to Alamo. As I'd read advice elsewhere to ensure that the voucher clearly said 'no 1-way fee' I asked and my voucher said just that. No problems at all.