Take a trip to Hollyrood Palace and then a walk up to the old observatory... great photo opportunities....
There are tons of great pubs in the haymarket area - I stayed in the haymarket at the APEX City hotel....
I got the hotel for $52 US on biddingfortravel.com
Apexhotels.co.uk also has some great deals.
Just take earplugs if you go to Edinburgh Castle when they fire off the howitzer.... scared the pants off me since I wasn't aware.