I tried to secure a block booking for APAT a couple of months ago, but unfortunately there is a huge race meeting that weekend and most of the hotels nearby could not accommodate.
My suggestion would be to book as early as possible if you are planning on staying in Edinburgh that weekend.
The Marriott, as Neil has said, is directly opposite the Casino but that, I was told at the time by their Manager, had very few vacancies, but still worth a try to get in there.
Edinburgh Marriott - 01313349191
Corstorphine Lodge Hotel - 08454566399
Tudorbank Lodge - 01313347845
Best Western Capital Hotel - 01315359988
Holiday Inn, Corstorphine Rd, Edinburgh - 08704009026
The last 4 are approx 5 mins in a taxi (approx £5 taxi fare)
Please note that these are just some ideas for you, I have been unable to secure any block bookings, but some hotels for you all to try.
Mary