Welcome to Prestonfield
Its in the SE of the city, around 20 minutes by taxi to Murrayfield or the city centre, but it's a fantastic place and has it's own helipad.
Not cheap, but if you can afford to fly a helicopter you can afford to stay there.
Someone once told me that their was a helipad at Edinburgh Castle, but if there is I wouldn't know who to contact or even if they'd let you in there.