when you arrive in Zambia, get a multiple entry visa.
The Zim side is worth at most a day trip - and its easy to walk across, and to the park which is just across the bridge. Then there is the tourist town (which was a ghost town when I was there, since its patrolled, and there arent any locals) - beyond that there is nothing really worth seeing.
I would really recommend staying on the Zambian side - maybe by the river - its very easy to organize trips into Chobe from there.
We drove from Malawi thru Zambia, and then into Chobe on the ferry, and onto Namibia from there.