We arrived fresh and early into Dubrovnik and got picked up at the airport by our first guest house - a place high up on the hill above the Old Town. Quickly unpacked, grabbed the wifi password and a map and headed down to check out the old walled city.
At first we wandered around, found the port and had an ice-cream. Booked a sea-kayaking tour for the next day and then went on a rather unusual walking tour. The guide was a lot of fun, bringing out terrible heavy metal puns and football jokes. Despite being a bit weird it was enjoyable and we learnt a lot about the history of Ragusa (what the Dubrovnik Old Town was known as when it was still a walled city). Would definetly recommend the walking tour, we did the general history one run by Marko, but there is also a Game of Thrones themed tour that will show you the filming locations. Last activity of the day was to walk the 3km city walls, you can see the whole city from every angle as well as the sea / nearby islands.
On other days we saw that the walls are extremely busy around sunset with literally hundreds of tourists trying to get photos of the setting sun. If thats your thing I'd recommend trying for sunrise instead.