If you want small, charming, fun to walk around in, good food, old city walls, architecture (including frescoes on exteriors), small canals and bridges, you could stay in Treviso. It's half an hour by taxi, or bus to the Venice airport, more like an hour by train. We did exactly this on one trip. When you look at Rome2Rio or wherever, be sure to specify the airport, not "Venice."
For a larger city with lots of things to see and do, with a wonderful market and lively piazze and the Scrovegni chapel, stay in Padua. It's an hour or less to the airport by train or bus. Padua is where we thought we'd like to live, after staying there for more than a week. We made a day trip to Venice itself by train (actually just through Venice on our way to Chioggia) and that was easy, so just taking a bus from near the train station to the airport would have been easy, too.
But it all depends on how early your flight home is --- many flights out of Venice airport are at 6:30am.