For serious walkers there are many good hills in Sutherland. Ben Klibreck, Ben Loyal, Stac Pollaidh, Ben Eighe, Ben Mor Coigach, An Teallach and the most northern of the Munros, Ben Hope, are all within reach.
Many attractive family walks are also available locally: The Fairy Tale Glen at Spinningdale, the forest walks at Ferry Wood Lairg and The Shin Falls, Carbisdale Castle wood, Skelbo Wood walk in Dornoch and the Golspie Wee Mannie and Big Burn Walk.
You may find these links useful:
http://walking.visitscotland.com/munros/
http://www.munromagic.com/CorbettMap.cfm
http://www.munromagic.com/MunroMap.cfm
Shinness is also on the edge of the North West Highlands Geopark. Look at the website www.northwest-highlands-geopark.org.uk to see a description of the extraordinary geology of the area and to find details of the guided walks that run from April to September in places like the Bone Caves of Assynt.