We stayed at Apostoli Palace for 2 nights in April and really enjoyed it. It felt like the only place in Venice that wasn't a rip-off. The room was very clean and nicely decorated, breakfast was included and excellent value. The hotel is very small and sweet with only a few rooms. The location is perfect - outside the main horrible tourist areas of Venice and surrounded by 'real' Venetian people, authentic shops and cafes. It is only a few minutes walk to Fondamente Nove boat pier, which has direct boats to the airport.
Only downside is that you have to pay for internet which is very expensive and you can only buy it when the staff are present, so if your credit runs out after 8pm you won't have access to the internet.