Jo, My favorite hotel, The Inverlieth is within your budget. I like it because it's a bit off the tourist track, but still close enough to walk back to. (I say walk back as I usually took the bus up the hill to Princes Street and The Royal Mile. http://www.inverleithhotel.co.uk
I took one of the Meercat tours--the Vaults--one year and really like it. I've been wanting to try the Rebus Tours. http://www.rebustours.com/ Of course, I'm a big Ian Rankin fan.
I like most of the sights. But I would particularly recommend The Georgian House and the Castle. I also did a tour of Holyrood (the parliament not the castle) which was fascinating. I enjoyed the walk along Leith Water too. If you want a nice day trip is to Stirling. The castle is spectacular.
The restaurants that I like include Creelers, Fishers, Mussel Inn, Stac Poli, and The Shore. Sandy's Bells is fun for traditional music.
Pam