Scotland is golf country, and Inverness is no exception to that rule. There are three courses in the city and if that's not enough for you, you can always travel to Nairn for their championship courses.
There is also plenty of fishing, hiking, and cycling to be had. Those interested in walking about the area should check Step It Up Highland, which has developed a series of different walks designed to get the people of the Highlands out and walking to promote good health. The Great Glen Way is a good area for walking and cycling, as well. You can do part of it, or undertake the full 73 miles in a 5 or 6 day trek.
If water sports are your thing, you can always try your hand at windsailing in Loch Ness (maybe you'll even get a glimpse of the infamous "Loch Ness Monster).
If you want to watch someone else play sports, rather than do it yourself, check out the Premier Division Footbal team, the Inverness Caledonian Thistle. There are also rugby games and cricket games to watch when you're tired of exerting yourself.
