We stayed at an AirBnb for the Roma game and the host gave us this list of good local places in Trastevere, the couple we tried were good and they highly recommended Suppli, but we didn't make it there. Meccanismo was a good bar with a good apertivo deal ( not sure if it was veggie).
A walk up Calton Hill will give you great views over the city and might be less of a trek than Arthur's Seat if you are only there for a couple of days.
Dean Village is picturesque and you can follow the Water of Leith Walk into Stockbridge.
The Queen's Arms on Frederick Street is a favourite...
http://www.southwalesargus.co.uk/sport/football/newportcounty/15561720.Flynn__I_wish_I_had_three_Ben_Whites__I_want_to_clone_him/
Ben White is getting some more rave reviews. Looks like an excellent prospect.