We book the flights direct with Virgin and the hotels direct with them (through our Amex platinum card service as we get a discounted rate, breakfast included and an upgrade on our room.) We like to stay mid strip, or if we are doing a split stay choose one at one end of the strip for the 1st part of the stay then move to the other end for the 2nd stay. This time we are staying at the Bellagio for a week but have previously stayed at the Venetian and the New York New York and I would stay at all of them again.
If you are just staying a few days I would stay mid strip, Bellagio, Paris, Ceasars are the more expensive resorts but Harrahs is cheaper and comes highly recommended on the Vegas boards I frequent. They have just re done lots of the rooms there and they are supposed to be nice. Ballys, Imperial Palace and Flamingo would be OK too.
I would not choose to stay at a resort at the North end of the strip, Stratosphere, Circus Circus, Sahara etc as 1) they are quite far out, the strip is a lot longer than you think and 2) they are older properties and are not so nice (except the Sahara which is OK) plus the walk from these properties to the rest of the strip is not so desirable later at night.