Hi, I know Edinburgh very well and indeed, lived there for a number of years. I love the Galleries and would look at it if i were you. The castle is also stunning. The historic venues have a lot of appeal.
hope this helps but in order to avoid boring others, happy to give you the lowdown in more detail if you private message me.
Lived in Central Edinburgh for a few years. There is a lovely little boutique hotel in George St, (One street behind Princes St.) so very central, its at the Charlotte Square end. The web link is http://www.tigerlilyedinburgh.co.uk/