I'm no expert, but as an ex-Brit with a interest in history, I can't say I'm aware of very much significant viking history in mainland Scotland. The Scandinavians pretty much kept themselves to the Orkneys, some other islands and small encroachments on the coast. That's not to say sites and artefacts don't exist, but many people are surprised to hear that the vikings left a much smaller footprint in Scotland than they did in England and Ireland.
Your visit to York is of course spot on. It has a lot of viking history with the bonus of fantastically well-preserved Roman and British history, too. Rather than go scouting for viking sites in Scotland however, I would suggest you spend more time north and/or west of York. Both Cumbria and Northumberland are littered with viking history and both areas were very significant in terms of viking incursions and settlement. The accepted wisdom is that the very first viking raid was upon Lindisfarne, which lies in that northern region. You probably know all this!
Probably out of scope this time, but i heartily recommend all visitors to the UK should include a few days on the Isle of Man, which sits in the Irish Sea. It's a great place to visit for lots of reasons, but it too has a strong viking influence and history.