There are a huge number of things to do in Edinburgh in August. You could actually say too many. There is the Fringe Festival with over 2,600 performances in cabaret, comedy, dance, music, opera and musicals, theater and spoken word. The theater performances range from dramas to musicals and can be fun, edgy and extremely well-done. Make sure to buy your tickets online before you travel. You can then pick them up at the central box office on arrival. Venues are scattered throughout Edinburgh, so try to plan your schedule accordingly as you can be running frantically all over town.
There is also the Edinburgh Art Festival, the Edinburgh Jazz and Blues Festival, the Festival of Politics, The Festival of Spirituality and Peace now known as the Just Festival, The Edinburgh Mela Festival featuring world music, fashion, dance and food, The Edinburgh International Book Festival and Edinburgh International Festival with a large number of offerings in opera, music, dance and theater. There are even festivals in magic and circus. The streets are jammed. There are street performers and musicians everywhere, with pop up art shows, food trucks and plenty of venues for eating and drinking.
The city is a great walking city. You will love walking the Royal Mile, stopping in for a coffee (yes there is a Starbucks), looking at beautiful cashmere scarves or buying your kilt!
Other neighborhoods to explore are in the new town on Rose Street and George Street with many shops and pubs. There are many shops carrying cashmere items. Walker Slater at 20 Victoria Street had some great quality menswear if you want traditional tweed.