Within walking distance the Apex Waterloo is the best quality but may be out of your price range- you get better deals if you stay for more than one night? Worth a look anyway.
On Royal Terrace just round the corner from the Theatre there are a number of older style hotels more likely to be within your budget: the Terrace, Royal Terrace, Ballantrae Albany.
Across the road from the Playhouse is the Holiday Inn Express (Picardy Place) - upper end of budget type hotel.
Within 10 minutes walk there are the King James Thistle hotel, Waverley hotel, Royal British and the Ramada Mount Royal all at the East end of Princes street.
You will have to read the reviews and make up your own mind!
Edited: 09 March 2011, 9:39