Surprisingly, one of Zagreb's nicest walks is around it's beautiful cemetery. Not as macabre as it sounds. It's easy to get there by bus, but is also a very do-able walk from the town centre. Gorgeous in autumn - buy roasted chestnuts and enjoy the views. Particularly lovely on All Hallow's Eve - October 31 - when people flock there to lay out thousands of candles on family graves.
Bus No 106 from the cathedral (takes 15 minutes) or tram No 14 from Bana Jelacica square