Whether you're looking for a loop or an out-and-back, Swauk Meadows offers an ideal outing just south of Blewett Pass.
It is possible to access Swauk Meadows from either Pipe Creek or Blewett Pass Sno-Park, but Pipe Creek is for non-motorized sno-park passes. Blewett Pass requires a groomed trails pass. Pipe Creek Sno-Park is also kitted out with a port-a-potty and a kiosk with rudimentary maps of the area. It's worth bringing your own, but you can supplement with these maps.
The loop is quite long for snowshoers, so many visitors simply do this as an out-and-back, staying left at the first junction and walking to the Blewett Pass Sno-Park before turning around and returning to Pipe Creek. This route parallels Highway 97, which does mean that you may be contending with highway noise.
Alternately, you can commit to a full day of snowshoeing (or cross-country skiing), and do a large loop. Here's how: From the parking area, head towards the east edge of the lot, where a snow berm will likely be piled up from winter plowing. Just over this berm, the trail starts, marked out by blue blazes, or diamonds attached to tree trunks. Follow these blazes for a little less than a mile to a junction. Turn right. This is Trail 141.2, which you can follow for 1.2 miles before arriving at another junction.
This junction marks a spur trail opportunity. To your right, a spur trail extends 1.5 miles, but there isn't much in the way of views as a reward down this way. Instead, continue on another mile, crossing an active snowmobile trail (look out for motorized vehicles.
At the next junction, turn left, and head northwest, paralleling and then crossing the motorized trail again. After a little more than a mile, arrive at the Blewett Pass Sno-Park. The Swauk Discovery Trail is here, which makes a great detour if you still have the energy. Otherwise, find XC 141 and turn left, paralleling the highway for two miles back to the first junction you saw. Continue straight on through this junction and arrive back at the parking area in 0.7 miles.