Lots of people finish their ride on the A9/A99. It the shortest. There are more scenic routes.
We did LEJOG a couple of weeks ago and I think we had a pretty good route
1. Having gone over the Dornoch Firth bridge we turned immediately right into Dornoch and then out via minor road to Loch Fleet whcih was spectacular with loads of seals lazing on sandbanks. This rejoins the A9
2. A9/A99 as far as Lybster. The traffic is OK on this stretch and the drivers all seemed nice and polite
3. Left at Lybster (actually somewhere called Occumster) and took the Camster/Watten road. Absolutely spectacular and you get chance to visit the Camster Cairns, some of the oldest Neolithic structures in UK
4. Via Lyth and series of minor roads, join the main road to JoG (from Thurso) at Canisbay and then you're only a couple of miles away
Left at Lybster is waaaay more attractive than the A99 via Wick. It's only 1 mile further so is probably quicker as you don't have to ride through Wick