As you aren't going to Falmouth the Cornish nationalists don't need to bother.
Invergordon is a cruise port, a naval port and an oil rigs port.
There is stuff in Invergordon but every one just gravitates south to Loch Ness and Culloden inevitably. There is a museum, the various HMS Natal memorials from WW1 (a disaster never fully explained), the Seaforth Highlanders in WW2 mural at the railway station,and the Polish Forces memorial, also the Dalmore distillery at Alness.
I was lucky enough to cruise in there post Covid when excursions were compulsory and socially distanced so we atypically did the Falls of Shin and the little cathedral city of Dornoch. Shin is best in the spring when the salmon are leaping. In normal times those are a taxi ride. And get the taxi to come back over the Struie scenic road.
You could also visit the Black Isle- Cromarty and Fortrose, and see the little turntable ferry across the narrows at Nigg. So there are options apart from the really obvious ones.
The distillery is possible by bus and I could (and have) do the Black Isle likewise, but hesitate to suggest the latter to a tourist.