LOVE that city and we are headed up next weekend for the bank holiday. I second the castle visit. The views are amazing from the top and its just a great great piece of history.
Climb the scott monument. It's a whole lot of stairs, but views are great the entire way up and you'll really get that blood flowing and boy, you'll feel alive
I've been on the meerkat tours as well. I loved it. Highly recomended.
One of our favorite places is the Grass Market district right under the castle. Its a nice side break from the royal mile traffic. I recomend the Beehive. Loved that place, roomy, and they had a beer garden last time i went.
Another one of our favorite places is the Malt Shovel just a skip away from the train station. I had my first pint after stepping off the plane here and it has a special memory.
I can also recomend Cafe Jacques down in the grass market a few stops down from the beehive. OMG the cakes there (as well as a tasty breakfast) were affordable and so so delicious.