phantom in vegas is a great show. of course blue man group and jumaji are awesome as well.
get a bus pass its like 3-6 dollars for all day to go up and down the strip and to get to fremont street. you are going in a pretty shit time of year its cold there and the pools won't be busy which are quite fun to drink and people watch. alcohol is stupid expensive so drink as much as you can in the casino, play some cheap slots and milk the free booze. hit up some buffets, i personally really like the buffet at bellagio.
for cheap hotels, luxor is usually on the cheap side, monte carlo, mgm. all teh hotels are going to look and feel the same just different decor. i personally prefer to stay at the hard rock off the strip and cab it to any place on the strip.
depending on your credit and how much you can prove for income one of the best thing to do which will save you money is get a casino host and start a line of credit at a hotel. do not use the line of credit to gamble, use cash. or whatever you have to gamble pull from the line and then pay the marker back with cash ASAP. this will get you free shows, dinners, vip and bottles at a club, and best of all free rooms. i can't remember the last time i paid for food or rooms in vegas and have enjoyed plenty of free comp'd bottle service.