I was in the same area last March. Here's my take on the areas you will be visiting:

London

We liked the Travel Inn County Hall for location. It has all the charm of a Motel 6 but it is clean, safe, and for London, cheap. It is within walking distance of many sites, including Westminster Abbey and Trafalgar Square. We really like to walk and actually walked from St. Paul's back to the hotel.

Edinburgh

We stayed at the St. Valery near Haymarket Station in the West End. We liked the location and it was very convenient to Princes Street and in fact all the sites. We did buy a ticket on a hop on/hop off tour bus.

http://www.stvalery.com/

No restaurant recommendations, our choices were pretty humdrum.

York

We stayed at the Sycamore, a few blocks outside Bootham Gate.

http://www.guesthousesyork.co.uk/

Recommended to do's include Evensong at Yorkminster, the ghostwalk that leaves from in front of the Minster, lunch or tea at Betty's, walking the Shambles, walking the wall, and several museums.

We traveled by train from London making reservations on http://www.trainline.co.uk Have your tickets sent to your first hotel--assuming that you'll be staying in London before taking off for Edinburgh and York.

With large English and Scottish breakfasts you can probably economize by eating only two meals per day.

Barbara in CT