What is your price range?
'The Bank 'on the Royal mile is OK, or 'Tailors Hall' in the Grassmarket - both on busy streets so be aware of noise in city centre. Both would be about the �35+ pp mark. 'Parliament House' on Calton Hill is nice and fairly close to the station. Rate around the �40+ pp and there is also a Jurys Inn - impersonal compared to some in town, but near very good restaurants, and pretty close to the station - overlooks it actually - but rates again about the �40+
If it is only a room you need, there is also an Ibis Hotel - about the �40 pp mark - a bit further out from Waverley, but ok to collapse into.
Info at:
http://www.visitscotland.com/accommodation/?vi ew=Accommodation or have a look through info at:
http://www.edinburgh.org/ for the Edinburgh site for other locations/rates.
Cheerio now.