We couldn't get into San Marco or the secret tour of the Doge's palace in mid May. Long lines for the former, impossible to get tickets for the latter. Maybe we planned it better but found a good time to see it in late October and managed to get tickets for the Doge's Palace secret tour (albeit in Italian only). It was still crowded but maybe a titch less.

Good thing about October is that all the seasonal cruises ships have migrated or are migrating for their overwintering grounds in the Caribbean by late October. We only saw, IIRC, MSC ships and Costa ships which may be based there year-round.

Advantage of Austria in October is that the fresh young wines are available at the city's heuringens and also the lightly-fermented grape juice.