Venice to Dubrovnik

"least expensive and quickest way" These are not always the same thing. Quickest will be to fly. Check http://www.skyscanner.com/ for options. If the one-way fares are too high, you can buy a round trip ticket and just discard the second part. In this case, flying may be the cheapest way as well. Dubrovnik has overnight boats to Bari in Italy, but then you have to get to Venice from Bari, which is almost 8 hours on the train. Here's a map of ferries from Croatia to Italy: http://www.find-croatia.com/ferries-croatia/ferry-map-croatia.html There are no trains to Dubrovnik, and buses would probably take days (look at the map and you'll see the distances involved).