We are flying out of Venice at 11:45 in the morning (flight to Ireland). We are going to be in Verona the day before. I'd like to stay overnight there and then take the train in the morning but is that going to be cutting it too close? I can't tell. Is there somewhere else closer that I should consider? We could stay in Venice another night but we will have been there for 2 nights already at the beginning of our Italy trip.
I'd stay in Venice. The closer you are to the airport, the better. Anything could happen to delay you from Verona. You can enjoy another magical night in Venice and not have to worry about getting up so early and rushing to meet a train to get there from Verona and can have a leisurely breakfast.
Staying in Padova is a possibility - there is a direct bus from the Padova bus station to the Marco Polo airport.
I'd also suggest Padova, as it's very close to Venice and has some interesting sights, including the Scrovegni Chapel (reservations compulsory). Two nights would be ideal there.
Padova sounds like a very good suggestion, with or without the Scrovegni Chapel.