Check out Tamarack Hotel in Tahoe City. it's pretty cheap - about $39 and is close to Squaw, Alpine, and Northstar (but who cares about Northstar). I stayed there while searching for an apartment last winter. Nice place with good service.
I wouldn't stay in Reno. The drive seems much farther than it is and can be a pain during storms unless you only plan on skiing Mt. Rose, which is a good place as well.
If you aren't too set on the North Tahoe, the South Shore has a bunch of cheap ass motels that you can stay in. Around there is Heavenly, Sierra, and Kirkwood.