Avoid if you can!
We're currently here renting a villa across the bay from the Old Town in Muo and Kotor is incredibly busy, so much so that what should be a 9 minute drive to the supermarket at 7 am ended up being a 40 minute journey due to the volume of traffic. Yesterday I gave up trying to drive to the roundabout that would take us out of Kotor and returned back to the villa.
Instead we walked the dangerous road to a restaurant 30 minutes away. Lunch was nice and we decided to take a look around the Old Town but with two huge cruise ships in port the crowds were huge and with the temperature in the mid 30's my tolerance levels were low so we gave up.
As for the cruise ships. The villa we are staying at has a balcony and pool terrace with oustanding views of the Old Town and mountains, that's until one of those obnoxious behemoths (or two or three) arrive and completely block our view. They sit there all day until leaving, the one yesterday choosing to sound their horn 10 times at 9 pm just to make sure that they had disturbed each and every person for miles around. Other ships manage to sound theirs only once once they start to move.
Unfortunately the town doesn't have the infrastructure to handle the numbers of tourists that it has attracted and the numbers are only going to increase.