Corstorphine Hill is the wooded one — the western height that does in greenery what Arthur's Seat does in bare rock. Edinburgh has hills to spare, but this is the one you walk into rather than up, under a canopy the whole way.
About four and a half kilometres, best on an afternoon when the light slants through the trees. Start up the Rest and Be Thankful, the old carriage path whose name tells you the Victorians took it slowly too. The oak and beech close over fast; within minutes the city is a rumour. Climb past the volunteer-run walled garden to Clermiston Tower, the square stone finger raised in 1871 for the hundredth anniversary of Walter Scott's birth — it opens only occasionally, but its foot is the high point either way.
Then the reason to come: a gap in the trees on the north-west shoulder where the whole Firth of Forth and its bridges lay themselves out. Drop south through the nature reserve and the old quarries, and land at the Corstorphine doocot, a squat 16th-century dovecot beside the old kirk. Bus 26 home from St John's Road.