Unfortunately, Strathpepper's main (sole?) tourism attraction, the Highland Museum of Childhood doesn't open in December.
Bus service 27 runs hourly into Inverness, with a journey time of 48 minutes:
http://www.inverness-scotland.com/
The route runs via Dingwall, which is just 22 minutes from Strathpepper. The town might be worth a visit but, once again, the museum will be closed in December.
Unfortunately, it looks like service 27 is the
only bus serving Strathpepper. You're considerably restricted in travelling further afield than Inverness by the time of the last bus back to Strathpepper. The last service runs at 1730 Mon-Fri, 1720 Saturday and 1545 (as service 19A) on Sunday:
http://www.stagecoachbus.com/timetables/2527_t t_2508wed13.pdf
However, there are much later services from Inverness to Dingwall (as well as the rail services mentioned below), which is only 3 miles from Strathpepper, so you could take a taxi for the last few miles without too much extra cost. If you plan on doing that, it would be wisest to book your taxi in advance, as taxi services in rural areas can be very limited. See here for phone numbers:
http://www.britinfo.net/taxis/TBBIP28050.htm
From Inverness, the northbound and westbound rail routes both go via Dingwall (so you could catch a train there, rather than at Inverness). The routes are both noted for being among some of the most scenic rail routes in the world. The westbound route goes right across to the Kyle Of Lochalsh. The northbound route serves Wick and Thurso, at the northernmost tip of mainland Britain. Timetables here:
18:27 Mon 20th Oct 2008