Go to the Last drop thats a pub I think it was Grassmarket and maybe your hostels offers a city tour Aotherwise walk down the street from the castel and make sure to visit some of the small sidestreets. I have been to some other place at the Grassmarket but I forgot the name and to an amazing club so going out is really nice if you like it. What is also nice is the small rock /mountain arhurs saddel or something like that You get a good overview there The castle should be nice but i didn't go there But was is nice is the Princess street and the park between princess street and the castle. And the rest just walk around and look into the small streets and places they are nice