There are plenty of flyers around Edinburgh.
You could also try Fife Flying Club, theres clubs in Cumbernauld and Strathaven is less than an hour away.
Today's Pilot - For people who fly
There are also aircaraft at Kirknewton, 20 mins from centre. I used to have a number for the hangar office, I`ll have a look.
You might struggle to get someone to take you up as they may not wish to confuse you by conflicting with your flying instruction.
I would reckon you will have a lot more luck once you have passed your test. There are always those looking to share the cost for longer flights.
Good luck.