I am wondering if it is possible to fit both of these activities into a single morning - I have no idea how long it takes to go through the Accademia and St Mark's Basilica. I know there's a lot more at St Mark's square area, the plan would be go to Accademia, then go through St Mark's Basilica, get lunch, and see the rest of what is around the square. Does that sound doable? About how far a walk would you say it is from the Accademia to St Marks?
Its maybe a 15-20 minute walk. As far as both in a morning, if you just want to breeze through the Accademia and check it off the list, I suppose so. If you really want to see the collection, I'd give it a couple of hours at least.
You can do both in one morning but I would allow at lest 90 minutes for San Marco and a couple of hours for the Accademia.
If you go up in the balcony of St. Marks and watch the sun play off the gold mosaics you may get mesmerized and stay longer than you think. the Basilica itself is quite a place. If you tour the doges palace and wander around the square you will eat up time. A twenty minute walk to Accademia sounds about right.