North towards Ullapool, and the far north
There is a roundabout near the football pitch at the far north corner of the city, within view of the bridge, through which the A9 runs. A short ways up from this there is a large area to pull over. If you are headed for Ullapool, ask to be dropped off at the roundabout where the A835 begins, just 6 miles from Inverness.
South along the A9, toward Perth, Dundee, Edinburgh
The A9 goes through the Cairngorms National Park, so traffic will be backpacker-friendly, and most will be going directly to Perth. Near the roundabout mentioned above, stand at the pull-over area on the appropriate side of the road. Cars will (in theory) be slowing down for the roundabout, and you will be able to see them as they come off the bridge in the distance. A sign is necessary here, as this is where traffic is scattered in several directions. If you are lucky enough to be hitching when a football game is being played, walk around the corner when it is finished and stand with your sign where the cars are trickling slowly out. Hopefully the visiting team will have won, and the fans driving south will be in a good mood!
Personal experience: TonyPro spent 5 hours over 2 days standing here in freezing rain. Drivers occasionally pull over here to look at maps; eventually he got a ride by asking one of them. Clearly this isn't an ideal place to hitch from, so take advantage of the approachability of the Scottish people. Other options are another pullover area about 1 1/2 miles down the highway (people will be going extremely fast there, but will all be going long distances south), or if you have a sign, outside the furniture store near the Thistle hotel, across from the KFC. And as always when taking advice from HitchWiki, keep your eyes open for better places.
For Glasgow, the A9 is probably the fastest route, but you may have better luck hitching the tourist route down the A82, along the edge of Loch Ness. This is also the way to get to Fort William.
East toward Aberdeen
Hitch from the roundabout outside the large shopping centre at the east edge of town, where the A96 begins (ask someone where the Tesco is). If possible, ask whoever is dropping you off in Inverness to take you here, because it is a long walk from the town centre. Just after the roundabout there is a bit of a sandy shoulder where people can easily stop. NB: Aberdeenshire is difficult to navigate hitchhiking, as most people are only going short distances. If you want to get to Dundee or Edinburgh, it is far better to go down the A9.
Accommodation and Sleep
If you don't mind the sound of highway traffic, there is an undeveloped area of scrub and trees across the A9 where one can camp. Either across Kessock Bridge or east along the A862, there are more secluded woodlands.