Jim,
My course (Brahan Golf Club) is just outside Dingwall north of Inverness. We are a 9 hole pay & play course with two sets of tees and two flags on each hole and the course will be reversible by this summer. You would be more than welcome to play and if you are looking for accommodation we have a guest house on the course.
As for recommendations I will stick with courses close by.
Royal Dornoch, Brora and Castle Stuart are obvious choices. Golspie, Moray (old & new), Nairn and Tain are all worth consideration. For not so well known ones then Spey Bay and Cullen are both fun courses.
Inland ones to consider would be Strathpeffer, Boat of Garten, Granton on Spey and the new course at Aviemore. For nine holers think about Portmahomack, Covesea, Ullapool, Bonar Bridge, Fort Augustus, Carrbridge and Abernethy.
There are lots more but any of the above will not disappoint.
PM me if you want help with finding accommodation or tee times,
Jon