A gang of us stayed in the Raddison when we were over for a couple of matches last year. Super location in the old town on the Royal Mile. Hotel was fine and would recommend it for location - rooms spotless, staff grand etc. Breakfast was busy but very good. Only one problem in relation to the booking. We had booked 5 twin rooms directly with the hotel and arrived early so rooms weren't ready. Returned later that evening to discover there were only 3 twin rooms left and one single ! Not even a fold out bed available - so the 2 smallest lads shared a small double bed and got a good few quid off the room but be warned !!
Edinburgh is truly beautiful and look forward to returning with missus for a non sporting weekend !
If budget is an issue and you are a member, I can highly recommend the Edinburgh Central Youth Hostel. They have 2, 4 and 6 bedded rooms and all have ensuite. Excellent facilities, on-site cafe, wi-fi etc., in walking distance of High Street/Royal Mile.
I have also stayed in many places in Edinburgh, including the Carlton which is very good. However as Phoenix says the Sheraton is hard to beat.
BTW theres so much to see and do in Edinburgh its best to plan your stay so you get to see everything. Worthwhile getting a day pass on one of the open top busses and also going out to see the QE2 - about 15 min trip by bus/train. Its permanently moored beside a large shopping centre with loads of restaurants etc.
The Glasshouse on Leith Walk is also very good but maybe not as central as some of the other hotels - its a 5 min walk to Princes St and 10 mins to Royal Mile
I can also recommend the Royal Garden Apartments on Queen Street if you're not looking for 5 star - decent apartments available for weekends and very very friendly and accomodating staff