We stayed with our two small children (6 months and 4 years old) for a week at Paola's appartment and enjoyed our stay very much. The flat is situated in a charming and (normally) quiet neighbourhood, if it is not European Soccer Championship :) within a 19th century villa-area close to the beach. It's only four stops with the bus to the Vaporetto-Station, so San Marco and all the sightseeing spots are quite easy to reach.
If you stay there, you can use the beautiful garden to relax for "siesta" after your sightseeing trip, which we did every day.
As others have already stated you can hear the people upstairs very loudly so if you are not used to "upstairs-noises" this appartment might not be your best choice. But one has to state, that in the night, there is hardly any noise.
The kitchen is quite small. There are only two hotplates (gas) and there is not enough room to use a pan and a pot at the same time. So it is not possible to cook elaborate meals. But there are nice restaurants (fE Bistro Glamy) within walking distance.
Enjoy a Spritz on the Lido!