the fact that you can't gamble or drink and its winter so maybe no lying the pool either
will mean you won't get the most out of vegas. nothing wrong with trying the white knuckle rides on top of the 1149ft stratosphere tower on the north strip though. northern nevada has lake tahoe which is really nice but the later you leave it the more chance roads in and out will be closed.
Grand Canyon Village at the south rim is the most accessible and most famous viewing point, lots of hiking trails near there too.
make sure to visit the big 5 in southern utah (arches, zion, bryce, canyonlands and capitol reef), Moab is a good base in utah with which to achieve this; personally i think Salt lake is a lovely city and well worth a visit; i wouldn't go out of my way to visit Phoenix
btw the best time to visit the west is spring, death valley is a sight to behold around march/april time