Your gonna have a BLAST! Nothing like Vegas! IMO I would have recommended a more mid strip hotel, but it will just mean a little more walking. Good move not getting a car, you don't need it. Plenty of Taxi's, The Duece, monarail, and just plain walking- just remember in Vegas things are never as close as they appear to be, just walking across the street might require you to walk down the street, take an escallator, bridge, etc- leave enough time to get from point a-point b... There is so much to see and do, without shows for your first trip (and only 3 days) I would say skip the shows, you can visit all the hotels, see the free shows, next trip I would plan some shows, but if you are sure you want to do shows- my recommendation would be "LOVE" & "Jersey Boys" IMO they are the best shows there- both excellent.
As far as eating goes, there are waaaaaaaay more places than you could ever recommend, I would say you should play it by ear, just see where you are and try something that looks good- all places have the menus outside so you can look and try it. I personally wouldn't weigh myself down with appointments/show times/reservations for 3 days, believe me, you will find something that looks good everywhere you go in Vegas! Have a blast!!! Feel free to ask away if you have any other questions!!
**added- BTW, weather in Jan could be very unpredictable, I would bring layers and lots of them, it could be 60 and it could be 20 and believe me, when it's freezing there its' REALLY COLD!! prepare for everything!!