I wouldn't book your room yet. Sign up for the email deals at all the hotels you might be interested in, and see what kinds of deals they are going to be offering for that week. That week is the least busy time of the year, so you should be able to get some fantastic deals. Start thinking about looking for a room around Nov 1st. The hotels should start putting out their December deals around then. And when you look at the price of a room, be sure to add in the resort fee. It won't be in the room price you see in the offer, but every hotel you look at will have one.

Also reconsider the rental car - you should be able to get a fantastic rate for that time (and after booking keep rechecking the rate - if it drops you can change to the lower rate). It will cost you at least $20 plus tip just to get each way from the airport, and if you only take a taxi one or two more times during your trip, the price of a rental car will be cheaper. The hotels all look close together, but it is deceiving - they are huge and it takes a lot of walking just to get from one to the other. With a car you then have the flexibility to go check out downtown, visit some of the off-strip casinos (Red Rock, M, Green Valley, etc), and I would even recommend a trip out to Red Rock Valley National Park for something different.