btw campsies are fine in the dry, you could head up, dumgoyne or up to earls seat too(gairloch hill is as far as you need to go height wise).
campsies can be mushy after rain though.
better to drive though, you can get a bus right out to wheel craft and up cortmalaw, talking 45 minutes from city centre though.
kilpartricks probably the easiest/closest without a car.
you’re looking at 35 minutes or so train to bridge of allen for dumyat, and about 1 10 hour out to arrochar, but you can get to proper mountains then, ie the arrochar alps.. got a mile or 2 to get on the cobbler path though round the bay.
One thing edinburgh has over glasgow is the big hill in the middle of the toon!
you could make up upy downness out in back mugdock. the back of the hill to south of strathblane.
edit: guess you could also just go and run the commonwealth track too up cathkin braes. just the number 20 from glasgow city centre and headin through castlemilk/fernhill. (take a chib 😆 )