In reply to kevin stephens:
Arthur’s Seat; Portobello Beach; Botanic Gardens; Modern Art Gallery; Chambers St Museum.
Cafe Royal pub is very very nice; 10 min walk away is Calton Hill which is pretty cool for such an easy walk.
Some of those things ARE very touristy, for the simple reason they’re great things to do.
if pissing down, climbing walls with nearby food/drink include
Alien Bloc (Crumbs cafe- best tortilla in Edinburgh and a local secret)
Alien Rock - first dedicated wall in the country (Porto & Fi, great fish pie, salmon quiche, and a nice wine list)
Eden - a bit out of town but nice coffee and cake, burger van outside and… IKEA? (Secret Garden cafe if u have a car)
EICA Ratho - amazing James Bond villain’s lair, great (route-)setting, quarry and canal. However, 5 miles out from city edge. Bridge Inn at Ratho is nice, 15 min walk from EICA and has a bus service back to town.