Once your are in Dubrovnik you should definitely take a Cable car ride to the top of Mount Srdj above the city. From there you can enjoy the amazing views of the whole city, the Elaphite islands and the Adriatic Sea. Cable car ride is a short and in only 3 minutes you will be at the top of the Srdj.
There are Panorama Bar & Restaurant if you wish to have a drink or dine while enjoying amazing views of the area. If you are after some fun you can take a buggy ride and explore hidden corners of the nearby countryside.
While there you can visit Homeland War Museum in the Fort Imperial to learn more about recent Dubrovnik's history.
For a huge choice of amazing SMALL GROUP and PRIVATE tours for exploring Dubrovnik visit VIATOR web-site and GetYourGuide web-site (Free Cancellation & Mobile Ticketing).
It is very easy to reach Dubrovnik Cable car from Old Town or Pile or Ploce Gates. From both gates you can reach it by walking around the city walls. There are pedestrian sidewalks which are not very steep and it is quite easy to walk towards cable car (8-10 minutes).
From Old Town you can do this by walking up the stairs from Stradun by taking Boskoviceva street. When you reach the top of the street you need to walk across parking lot towards stairs below cable car.