Suggestions welcome for our short stay (7a - 6p).
If you're on a cruise ship port of call, you'll probably be tendering in, so build that into your available hours. There's space for one ship, depending on its size. If there are more than one in port, it can take up to 20 minutes to tender in.
Here are a couple of suggestions:
Hire a local guide to guide you in Kotor, and outside of town if you have the chance. Tours by Locals offers several options. At least drive up the serpentine road for views of the Bay. There is public transportation but a taxi and/or guide is the easiest way to get up there. Perast is scenic and pleasant, and the attraction of Our Lady of the Rocks has got an interesting story. We thought Herceg Novi was dull, as was Budva.
Stay in Kotor without a guide. It's a sweet little town that's charming to walk around in. The streets are mazelike but you can't get too far lost. It's got a Cathedral of course, and couple of interesting churches, including an Orthodox Russian (I think) that we stumbled on while strolling. The priest there was very happy to show us around and answer questions. The town walls are a hike, but the views are worth it.
Undertake a ship's excursion, especially if you want to get further inland without hiring a local guide. Public transportation is not worth the time it would take you to figure out.
Unfortunately, Kotor goes from charming to badly clogged when a ship of size is in port. My guess is that the deeper you go into the historic core (away from the water), the more pleasant it will be.
I liked both Herceg-Novi and Budva. I'd prioritize Herceg-Novi over Budva since Budva reminded me more of Kotor, and getting to Herceg-Novi will take you around a chunk of the extraordinarily scenic Bay of Kotor. That ride would be my top priority on a trip to Montenegro.
At least drive up the serpentine road for views of the Bay.
The views are spectacular. However, the road is steep with solid rock on one side and nothing on the other. There are dozens and dozens of 180 degree switch back turns, and many, many other turns. It's large enough that large vehicles drive it, but if you or anyone in your party is prone to motion sickness or has a fear of heights, it might be better to avoid the road. You can do a google search and also use google maps to check out the road to see if you want to travel it.
If you are able to take a short/steep hike - St. John's Fortress above town offers unbeatable and breathtaking views.