You could take the A87/A887/A82 to Inverness, then the A9 to Wick. That would involve about seven to eight hours of driving. It would be mostly scenic, especially on the way to Inverness, and most of the way through Flow Country up to Wick.
However, my personal preference would be to take the west coast route through Lochcarron, Gairloch, Ullapool, Lochinver, and Durness, and then head across the top of Scotland, through Tongue, Bettyhill, and Thurso. By going that way, you would see some of the most spectacular scenery on Earth. You could even attempt the Bealach-na-Ba to Applecross, then drive around the peninsula via the coast road to Shieldaig. Going by the west coast route would take you two days. Best places to stop would be Lochinver or Durness.
To be honest, I've never stayed in Wick. It's not the most attractive of towns, although the harbor area is fairly reasonable. It's not considered a "tourist" town, although there are a couple of (free) castles and the Old Pulteney distillery. I haven't been to it, but the Wick Heritage Centre is supposed to be quite nice. The Lonely Planet Guide recommends Mackay's Hotel, but you could go on Trip Advisor and check out reviews for the various hotels and B&Bs.
Good luck to you!