We really enjoyed our stay in Grazia's apartment. It's located in the northern part of Ortigia, with plenty of parking lot options nearby (we parked just off Ortigia, across the bridge). The apartment is in the middle of a lovely, quiet little side alley/street, and a stone's through from the mercato that happens every morning on Via de Ortigia; it's also a very short walk from a taxi stand if you need to take a taxi anywhere (e.g., the archeological park or museum).
Though nothing in Ortigia is more than a 15 or 20 minute walk from anything else, so you can't really go wrong.
One of the beds is located up a spiral set of stairs in an open loft; there's a half-bathroom up there too, and then the other bedroom is right by entrance and isn't fully enclosed either: there's a bulky/long room divided/store unit that makes up the "wall" of the bedroom. Despite the fact that neither bedroom is completely enclosed, you can still have privacy as the two bedroom are some distance from one another. The washer was pretty easy to use (just make sure the door to the washer is actually locked in to the machine before you start) and Grazia has a drying rack on the balcony that came in handy.