we had a very nice stay in Venice, with our 2 children (12 and 14). Mina's flat is convenient and clean in a quiet area 10 to 15 minutes walk to San Marco's depending on your hability to choose the most straightforward route ! ;)
Mina provided all the basic stuff to let you settle down not worrying to go the market straight away. The nearest Coop supermarket is 5 minutes walk though!