Ex Killin resident here.
Loads of walking in the immediate area, don't get in the car and drive an hour to Dunkeld!
Snow may be your deciding factor here, ask at the outdoor shop on high street for latest conditions.
'Easy' Munro's in area
Bheinn Ghlas and Ben Lawers - a straightforward trip, you start at serious height already from car park. Lovely view from top.
Tarmachan - brilliant day out, but steeper in places with a couple of proper scrambles, and return back through col is a trackless bog hop to the track.
Some less well know family wanders:
Sron a Chlachain ('The Cheiftans Nose') is the hill from the park in Killin with amazing views down Loch Tay. Brutally steep - but short and fun for kids. Ours did it from age 4....
Beinn Leabhann - is the hill to the East of Glen Ogle pass car park. You can follow a track all the way up to mobile phone mast, with only 500m or so of distance over rough ground to top. Again, you start high, so lovely walk up with amazing views.
Meall Odhar and Creag Garbh - are the two hills to East of Lochan Breachlaich, which is South East of Killin. You walk from village through the woods, up the old hydro road as the view suddenly opens at the dam. Lovely track around and a few hundred metres of hill path to the top of Odhar. Really nice walk ( a family favourite), with shelter and views around the dam area for picnic, and no-one gets fed up of exploring the dam area (take care, some big drops into cold water).
Lower level walks
Auchmore has some ace walks - starting at the viaduct over the river, you can walk around the stone circle, pick up some 'hidden' paths around Auchmore Burn bridge which then take you up alongside the stream all the way to the top forest path. You pass multiple waterfalls, under road bridges, through different woodlands. Bonus points if you can find the secret 'Infinity Pool' - a heart shaped swimming pool with its own 20' waterfall. shhhhh.
Head of the loch walk - great walk past Killin Castle (scene of the Black Knight from Search for the Holy Grail), along old railway, sandy beaches and more. All marked locally.
Glen Lochay is deserted, even a walk along the road above the power station is just lovely, all the way up to the end of the proper tarmac. Waterfalls, woodland, peace. Enjoy - even better as a bike ride.
Finlarig Waterfalls (and Lochay Waterfalls) are actually the older tourist attraction than the Falls of Dochart. The Lochay falls are now cut off by power station and dangerous to try and access. Finlarig (Alt Na Chruinn) are lovely - park at the holiday park cabins on the North Shore, just past the Golf Course. You can follow the paths and forest roads up the hill, until a particularly steep corner reveals stunning waterfalls, best after it has p*ss*d it down for a day...
'Oddities'
Hire a canoe and go to the islands for a proper escape - take the stove and bacon butties with you, stay deserted and explore.....
Falls of Acharn (East end of Loch Tay) - great wander around fabulous waterfalls, complete with caves. Even better, can you find the Cave of Caerbannogg from the Killer Bunny scene in Search for the Holy Grail on the way home....
Visit the now deserted village of Old Lawers - park in Lawers village at the pub, walk down the obvious track to loch shore. At loch you will find main village to the East (go over the bridge and find the graveyard) and old steamer jetty to the West. My kids loved that beach and old village. Google the Lady of Lawers for added spookyness....
*if* the mountain road is open and gritted (it may be 10' deep in snow still), then the trip over to Bridge of Balgie by car or bike is a cracking day out, loads of walks and places to explore in Glen Lyon ('the Longest, Loneliest and Loveliest Glen in Scotland")
Some pics to whet your appetite...
https://www.flickr.com/photos/matt_outandabout/albums/page3 How much more do you want!?