And if you take advantage of your stay in Edinburgh to broaden your horizons?

In Edinburgh

Visiting an art museum in Edinburgh. Most art museums have a free entrance policy and they have some pretty good collections, particularly the National Galleries, the National Museum of Scotland, the Royal Scottish Academy.

Just downhill of New Town and attractively straddling a river near the elegant Royal Botanic Garden, it’s small wonder that Stockbridge became one of the city’s first hip neighbourhoods. It’s now one of Edinburgh’s most desirable, though many bohemian touches have fallen away as its residents have matured and the area has gentrified. Some second-hand shops cling on, but mostly residents display refined tastes in basement bistros, gastropubs, coffee and antique shops, boutiques and delis and at the Sunday farmers' market.

Near Edinburgh

Visiting St Andrews, a picturesque town nearby the sea (see for details here.), and it only needs less than 1.5 hour to get there.
St. Andrews is a seaside town northeast of Edinburgh, on Scotland’s east coast. It's known for its many golf courses, including the Old Course, with the landmark Swilcan Bridge at the 18th hole. The British Golf Museum chronicles the history of U.K. golf. On a headland nearby are the ruins of St. Andrews Castle, with its medieval bottle dungeon. Close to the castle is the University of St. Andrews, founded in 1413.

Fife has charming villages and towns including well-known St Andrews. Dunfermline has helped put this region on the map, with it's new city status as part of HM The Queen’s Platinum Jubilee.
Information here.

Visiting Roslin an historic and very famous village which happens to be very close to Edinburgh (~45 min with public transport).
Rosslyn Chapel, formerly known as the Collegiate Chapel of St Matthew, is a 15th-century chapel located in the village of Roslin, Midlothian, Scotland. Rosslyn Chapel was founded on a small hill above Roslin Glen as a Catholic collegiate church in the mid-15th century.