Botannic gardens worth a wander if the weather is dry. AMAZING chinese not too far from zoo is The Chinese Manor House (that is about 3 miles out from city centre though)
And there's a fab italian near Chambers st museum called Chio Roma on South Bridge st (that is the st that Chambers st ajoins - not the Greyfriars bobby end - the other end of Chambers st)
If memory serves me right, restaurant is directly next to a Tesco Express.
Calton Hill gives decent views and if you are shopping in St James Quarter, grab a coffee in the top floor cafe of John Lewis. Window seat views are fantastic.
Royal mile has castle at top, Camera Obscura (good clear day only)
St mary's close. Go under edin streets and find out about old tenament living conditions
Museum of childhood - free
People's story museum - free
Chocolate experience just off bottom of royal mile pre booking essential.
Or do a bus tour.
You will find lots to do.
Go up Scott Momument in Princes st gardens