Dubrovnik has become extremely popular in recent years and the infrastructure hasn't quite caught up. The real problem is when the enormous cruise liners arrive and disgorge their passengers en masse into the small old town. These beasts are like small floating cities, and the passengers are ferried in non-stop frenzy of activity. Hundreds of Filipino sailors shuttle the masses back and forth in an endless stream of orange boats.
If you arrive when one of these is unloading, or god forbid two, then you will hit a wall of humanity as you enter the city. It really will take the edge of your enjoyment as you fight through the crowds, although even on a very busy day you can find some quiet spots if you move away from the Stradun. Most of the cruise passengers just seem to want to march through the main sites on the Stradun and march straight back out again.
You can avoid the worst of it.
The port authority recognises that the cruise liners can spoil the atmosphere of the town, and so have limited the numbers allowed. They also keep a schedule of when cruise liners will show up and how bad the crowds will be. You can use this to plan when you want to visit the old town, and when you might want to go somewhere else, like Cavtat. Check the link below.
I cannot even imagine how upset I would be if the streets were packed with bus loads of tourists along with a cruise ship of two that hit the port. That literally would bring in maybe 5,00 tourists to fill the streets and make everything too congested and hard to move around. This is the reason we chose off season months, and April/May was okay. Dubrovnik is so popular for all to see now that it is not for my claustrophobia and unpleasant ventures.
The main Stradun ulica is somewhat narrow and short in distance, that also includes the whole town, so once crowds get into the middle, it has to get jammed up.
Dubrovnik is beautiful, but I was disappointed in one respect: there is no normal local culture there. The only Croatians in there were serving the masses of tourists that swamped the old city. The shops sell the same mediocre tourist fare you will find at any international tourist mecca. The ambiance was a little disappointing. I went there in June.
Even before high season, we found Dubrovnik unpleasantly crowded. The old city is quite small (you can walk all around it in an hour or two) and the tourists are packed into its walls like sardines. While there was plenty to see, the hordes of people made every sightseeing opportunity a bit of a struggle. If you must go during high season, I recommend visiting Dubrovnik during mid-week so as to avoid as many of the regional tourists as possible.