To avoid the rugby on Saturday, if it’s dry, you could drive to south Queensferry and get a boat to Incholm Island. Or have a wander through Dalmeny Estate (there’s a loop you can do - search online - takes a couple of hours.
Dean bridge/water of leith/stockbridge wander is lovely. Plenty of cafes, restaurants etc.
Go up Carlton Hill, short walk, view over the city, opportunity for some nice pics.
Watch out for the Christmas decorations outside The Dome on George Street.
food wise, in no particular order Baba, indigo yard, Lady Libertine (the ground floor cafe), Black Ivy (if you go for a wander in bruntsfield/morningside), the Raeburn, Kings Wark (Leith), The Raeburn or Hamilton’s (Stockbridge), Mowgli, Fava, Bonnie & Wilde (St James Centre - close to Carlton Hill).