I love the St. John restaurants (of course).
Sweetings is an old, old school emphatically seafood focused restaurant - perfect for lunch for the food and the experience.
Shoreditch / Hackney is happening right now (where 259 Hackney used to be). - Rochelle Canteen is an brilliant place for lunch - especially if the weather is nice (ha) - book ahead. Upstairs at Ten Bells is above a bustling pub, serving elegant, interesting food and a very solid wine list (I drank the Frantz Saumon Mineral + there). Clove Club is great too - only serving a prix fixe menu in the back, but a la carte in the bar area.
Another wine shop worth a visit if you head up to Broadway market is Noble Fine Liquor - hit the market on Saturday, eat food around the market, pop into F Cooke for an old school pie and mash experience, buy some wine from Noble Fine Liquor, walk along the canals.
Walking along Columbia Road on Saturdays when the flower market is on is worth it too - beautiful old street with small houses and tiny shops only open one day a week (how does that work?).
Borough Market - Thursdays are good - get the chorizo sandwich from Brindisa + Monmouth coffee, Neal's Yard Dairy.
Tate Modern Museum + walk along the Thames and grab a drink sitting outside at the top of the Oxo Tower (expensive, but great view).
Cocktails? That's a whole other list.