I'm going to the Highlands myself in late May/ beginning of June for 11 days
My hands on knowledge of the highlands is limited but I could give a few suggestions based on what I've got planned.
If you've never been to Scotland before one of the mountains that is probably on every tourist list (and probably alot of walkers) is of course Ben Nevis. Piece of advice though. Me and some friends tried it last year in August and found that the route is constantly packed in good weather (you'll probably never meet a busier mountain) so if you're competent and feeling up to it I'd suggest heading up from Fort William to the summit of Carn Mor Dearg and from there along the arrete up to the summit. There's a fair hold hike up from the CIC hut (I think it's roughly 1800-2000 ft but i may be wrong) which is fairly steep but not overly troubling if you don't stray too far to the right as you ascend.
Another area I'd suggest if you're competent on steep ground and ridge walking would of course be Glen Coe which despite the various dangers (as illustrated by last weekend's tragic accident) is in many opinions the most spectacular Glen in Scotland and contains many good walks such as Bidean nam Bian and Aonach Eagach, the narrowest ridge on mainland Britain.
The Mamores which sit at the southern end of Glen Nevis could also be worth a shot with both sloping and narrow ridges and a decent variety of terrain from what I've been told.
And if you really have a thing for castle-like mountains try venturing to Torridon which is choc full of spectacular climbs and airy ridges such as The Horns of Alligin, Liathiach and Beinn Eighe.
Finally, another popular area is the Cairngorms which unlike their western cousins are more sloping in shape but form a vast plateau with several of Scotland's highest peaks contained there including the second highest, Ben Macdui which I can personally recommend from experience as a delightful mountain in good weather (the little of it you'll find there anyway
).
As I said I'm only of limited experience having done two trips to Scotland (First being the Cairngorms and the second being Glen Nevis) so take my suggestions with a pinch of salt but I'm wherever you decide I'm sure you'll have a great time