Place to sit a while in Dubrovnik

The Buza Bar would be a treat place to kill some time if it's open. But my guess is your friends will walk the walls in the morning?

There are many cafes along the stradun (Main Street) where you could sit and just have a coffee, maybe a piece of cake. Also, just next to the clock tower, at the end of the Stradun is the Gradska Kavana Arsenal Restaurant where you can sit and people watch. We sat there one afternoon and had cheese and crackers with some nice wine. They do not rush you.

Buza which means hole in the wall. Takes a little effort to find it but worth the hunt. You will be hanging on the outside of the wall. Spectacular view and experience.

as others have said above, Buza Bar has spectacular evening sun views. get a beer, find a spot on the cliff and enjoy the sea.

the other place i would highly recommend is Gradska kavana Arsenal. the food is good, service is fantastic. its a huge restaurant/bar. you can sit outside in two places: either by the harbor side outside the walls and watch the boats and city or inside, by the central square within the walls. the indoors are great as well, with several different ambiences to choose from

You might want to visit the Buza bar when your friends are finished the wall

Some go to the Buza Bar. I like the Buzz Bar. It's on the hill side of the Strada. Always cats there, and the coffee is reasonable. In the afternoons, they have a happy hour.