ah, a single digit postcode; jolly good. Welcome to the neighbourhood
I'm just along the road, in Newhaven. North Edinburgh is a bit of a desert for decent suppliers, so we go to Bower's in Stockbridge for meat. Mark is the owner - very helpful fellow. Armstrong's across the road for fish. Tattie Shaw's at the top of Leith Walk, or Mr. Akram's in Stocky for veg, or you could try one of the box schemes. I'm not mad on them as there's only so much beetroot and mystery greens that I'll eat.
The market is on every Saturday - it's a bit expensive, but I sometimes pop up for the German bakery. Their premises are otherwise in far and distant Bruntsfield. If you can't be bothered heading up there, sit tight until June - most of the producers there tend to decamp to the Links for the weekend(s) of the Leith Festival.
Your local supermarket is now the Co-op at the Foot of the Walk, so ditch your Clubcard for a Divi! Oh, and Lidl in the Kirkgate is being remodelled

You can get a Sunny Leith t-shirt (de rigeur in EH6) in the wee newsagents opposite Woolworths. The Kirkgate is also home of the riskiest meal in Edinburgh - a quarter pounder from the portable grill of a mad Polish guy. Delicious