Veronica's place is excellent. It's a little bit out the way but don't let that put you off.
If you want excellent accommodation in an area that isn't filled with tourist crap but authentic, vibrant, cafes, bars and shops, this is your place.
It's well connected on the Vaporetto, but there's not really even a need for it for most things. It's a 20 minutes walk to the centre and you'll pass several high streets and cool little areas on your way.
We stayed with our 9 year old boy and we had a fantastic time.
The thing I would advise is to store luggage close to the flat as soon as you get there, rather than in Piazalle Roma. There's a luggage storage one river away (about 200m) next to tons of bars and cafes, that would have served us better.
We couldn't recommend enough!