There's a bus that goes from Reno to South Lake Tahoe state line. If you stay there you'll get all the night life and Heavenly, Sierra, and Kirkwood ($10) all have shuttles to get you to their mountains.
Squaw, Alpine, Homewood, Northstar all have shuttles. Your cheapest bet to stay in North Lake is the Tahoe Biltmore, Cal Neva, etc. I think they offer like $29+/night rooms.
Well, we have different ideas of "North Lake Tahoe." CalNeva and the Biltmore are on the north side of the lake, but they are far from any mountains except Mt. Rose and Diamond Peak. Mt. Rose is a lot of fun with some insane steeps and a good laid back vibe...but their base lodge is at the elevation of most of Tahoe's other peaks. If you're not used to the high elevations, it may not be a good place to start your vacation. Diamond Peak is pretty but not challenging. It's advertised as a kids/family mountain.
From CalNeva your drive to Squaw and Alpine will be nearly as long as to Heavenly. It's a casino on the Nevada side, and Biltmore has a nightclub, but it's pretty low rent. If you want night life, just stay in SLT. If you want big mountains just minutes away, stay in Tahoe City on the northwest shore. That's where Alpine, Squaw and Homewood are, with Sugarbowl and Northstar not too far off. Tahoe City isn't a city at all, though. Very laid back Cal town, some nice restaurants but no nightlife.
And don't let them fool you...Kirkwood is NOT at lake Tahoe, though it is definitely a must-visit no matter where you stay. It's a fair distance off South Lake, and if the weather is bad you may have trouble making it in (or back out) across the Carson Pass. Oh, and the only reason we've ever stayed in Reno is because our flight got in too late to make the drive across the mountains to the lake...it can be scary in the daytime, but terrifying if it's late and you're tired.