So I posted a question regarding our week long apartment rental in Venice next March/April for DH, me, and our children aged 4 and 18 mos.
Here is the thread:
http://www.fodors.com/forums/threadselect.jsp?fid=2
I have 2 trains of thought. One is that we have a week and perharps staying in this wonderful area will give us the less of a tourist's perspective and more of an opportunity to really enjoy Venice. The second is that we have a backpack for our 18 month old but our 4 year old is on her own walking-wise...should we choose an apartment closer to the "sites"? Even if we have 7 days to experience Venice?

For some reason my computer was having issues pulling up the link to your other thread, but I will say that in the past i've loved wondering around the less touristy areas of Venice. It's a great place to soak up the atmosphere pretty much wherever you are. That being said, it's awfully easy to get lost, having to take some fairly indirect routes to get where you want to go. If you think you'd enjoy getting lost and exploring random areas, then go for it. If that sounds like a problem for you, or for your children, then maybe not.

The posted link it the general link to the Europe forum, not a specific thread. We can try to find her thread by clicking on her name . . .

I just topped it "Another Venice accom. question"
TIA

One thing to consider in the apartment itself is the number of stairs you will have to navigate. Our recent Venice rental was wonderful except it was 71 steps up and I can't imagine hauling kids up and down several times a day!