On an evening walk down Ness Islands in Inverness itself. There is some nice restaurants to enjoy dinner and drinks overlooking the river but you do need to book in advance normally.
Culloden battlefield is interesting if you enjoy history. The Inverness museum is free in town to visit and worth a look.
Loch Ness is lovely for a walk around and if you drive up to the very top of Milton of leys in Inverness you get a lovely view of the black isle and Moray Firth.
Down by the canal is nice to walk especially around Merkinch nature reserve but please only go in daylight as the tide can come in fast (you get plenty of daylight hours in May).
I personally prefer the east coast so up towards Dornoch as it's quieter but the views are also stunning on the west coast. The Black isle is lovely to drive around and Fortrose beach is nice. You often see dolphins at Channory point. Ord Hill has great views though is a little rough terrain wise so bring good walking trainers.
Highland folk museum is great if your driving up you can stop on route.
Aviemore is nice but very touristy. Loch Morlich is gorgeous but so busy on a hot day.
The midges are fierce in May in areas near trees so maybe bring some Avon skin so soft original spray as they dislike the smell.
Where in the city are you staying?