Captain Smithy is right. It's an absolute disgrace that Scotlands capital doesn't have a GA friendly airfield.
It is almost worth paying the price to fly to Edinburgh direct then Signature should give you a lift once you get there. However you must check they can accept you as they have limited parking.
Next nearest to the city is Kirknewton although dealing with the MOD in advance is an extra hassle. If there are no locals available to help you are kind of in the middle of nowhere.
Glenrothes, Cumbernauld, Perth and Dundee are next in order of distance. Dundee and Perth although the furthest have a stations and are busy enough fields that you will be able to blag a lift.
D.O.