Arthur's Seat and walk above Edinburgh. Can be steeper than you think. Super views on a clear day.
Botanical Gardens and walk along Leith. These are extensive and really beautiful. Pay the £5 to go into the glasshouses with a wonderful variety of exotic fauna.
Music - Organ recital at St Giles, folk music in Sandy's and singer at No. 1 High St. Plenty of music of different styles on offer of course.