The short answer: for the breakfast people write home about, book 23 Mayfield, for a treat within walking distance of everything book Crescent House, and for a warm welcome at a fair price book Castle Park on Gilmore Place or Sherwood on Minto Street. If you want a B&B in the city centre, know that there's barely such a thing: Elder York Guest House, 12 minutes' walk from the Royal Mile, is as central as a genuine B&B gets. Most of the city's guest houses are a mile south in Newington and Bruntsfield, about 20 minutes into town by bus. If you're still choosing an area rather than a house, start with where to stay in Edinburgh.
Every one of these 16 houses is a small independent guest house or B&B that serves breakfast in the house, and at most of them the owners cook it. Guest houses that are now room-only, hotels that call themselves B&Bs and self-catering flats are left out. They're grouped by area: the central-ish New Town and Calton Hill edge, the Newington guesthouse strip, Bruntsfield, Leith, and Portobello by the sea. Each card gives the same six things in the same order: breakfast, minimum stay, parking, stairs, the bus (or walk) to Princes Street and the walk to the Royal Mile, measured door to door to the Tron. Each area section links to that area's own hotels page.
One warning before you fall for any of them. Edinburgh's prices swing hard with the calendar: in August, when the Fringe and the festivals fill the city, and at Hogmanay, a room can cost two to four times the rates below, minimum stays get longer and the small houses fill first, so book six to nine months ahead for those dates. The prices here are dated off-peak midweek rates from each house's own booking engine or tariff, to compare houses by. They are not quotes.