What do you fly ?
Depends on what you fly as to what options you have, Kirknewton is Strictly PPR and whilst it used to be fairly GA friendly, now it seems anti GA (other than based GA)
But certainly worth trying contacting Cranwell to see if Permission is available (weekends are a 'no-no' though) THE RUNWAY THERE IS RATHER STONY & PROP DAMAGE IS A GAMBLE !!!
The Train Station of Kirknewton is about 1 mile away and easy walk, but in the village (0.5mile) you can also get the No 28 Bus straight into Edinburgh for £2.50
There are other nearby options if for example you were flying a microlight.