In reply to RX-78:
I live in Inverness - the Citylink services are running a normal timetable on Christmas Eve (917 Inverness to Fort William service and 961 Inverness to Ullapool), with the 917 normal service on Boxing day too (961 is reduced on Boxing Day, back to normal on the 27th). No service on Christmas Day. There are good walks accessible from those routes, it depends what you're looking for in terms of mountains or low level walks. There again, given the short hours of daylight, you may well prefer lower level walks nearer Inverness itself rather than aiming for munros.
Stagecoach operates the local buses, so you can get to local towns like Dingwall and Nairn as well as the Black Isle easily, take a look at the Stagecoach website for routes.
Regarding trains, it's still not clear what the strike situation will be. Strikes were or are going to be every Friday and Saturday in December, so that would mean no trains running in the Highlands. I've bought my tickets to get from Inverness to Edinburgh and then to Carlisle on Fri 23rd Dec and have a horrible feeling I won't be going anywhere. Strikes aside, the Kyle of Lochalsh line goes through great scenery, and the Wick line is useful if you want to do sections of the John o'Groats Trail.
The WalkHighlands website gives a good selection of walks in the area and for each route description also says what the public transport option is (if there is one) for getting to the start points.