general /
Closest Links Course to Birmingham
Royal St Davids at Harlech, Conwy are both superb. My return journey from Hillside was two hours so that is accessible too. Weston is not a links course so does not fit the bill and is not that special. North Wales GC is better, if not a links course.
With regard to flying to Inverness - I have done this for the last two years and it is extremely easy to get to Castle Stuart, Nairn and Nairn Dunbar from there. You just have a lot more hassle prior to getting on the plane.
The East coast is more awkward to get to so I would suggest the west is better.