For trail suggestions call the shop at the (530) number at the top of this page, or just stop by when you're here. Or for something you can check from afar, take a look at Mike's 'sticky' thread on the backcountry skiing sub-forum here at the top of the index, the one that acts as a guidebook and compilation of all the great backcountry skiing spots around the Tahoe/Truckee area. The same places are excellent for snowshoeing.
If I had to make a single great recommendation, or perhaps two...
If the weather's good, drive up to Tahoe Meadows on Nevada highway 431, a mile west of Mt. Rose Summit. Park at or west of the west end of the meadows and head south through the forest. In a quarter mile you start to distinguish a ridge ahead of you, which you head a little more to the right/west to gain the foot of, then you end up heading up this ridge while also heading south. By the time you're a mile out, you're on the Sierra Crest and basically have put yourself on the Tahoe Rim Trail. Soon you're looking out over the entire valley of Lake Tahoe on your right (west) and 4,000 feet down to the Carson Valley on your left (east). As far as you wish to go on that ridge, it just gets better and better. There are some good lunch spots where the sun has usually dried out some rocks and logs or possibly even dry areas of ground. You can make it anywhere from a 2 mile round trip to all day.
If the weather's not as good, but still worth going out, have yourself a nice snowshoe hike up the gentle canyon of Meek's Creek, about 20 minutes' drive from Tahoe City down highway 89 on the west shore. It's just a snowy valley with alternating series of big open meadows, creeks, and lots of pine trees. You won't be up high or have a big view to far away, but it's a fair enough thing to do on a bad weather day (as long as it's not a major storm).
There are zillions of alternatives, and that other message board thread of Mike's has many of them, or just call or stop by. Enjoy your trip!