I did a cruise on the Seabourn Spirit from Mumbai to Alexandria that made a two-night stop in Dubai. Incredible place - be sure you (at least) have a meal at the Bourj al Arab. I can never say enough good things about Seabourn! If you do decide to sail with them, they will spoil you for anything else.
Two couples from Mexico City (one had his own Gulfstream IV) joined the cruise there. He invited us to join him when we disembarked in Alexandria. That plane was fabulous!
LHT28 mentioned HAL in 2009 - I checked on that one last week while we were on board the Oosterdam and it wouldn't let the on-board agent book that segment (or any segment for that matter). I was interested in doing the Dubai to Cape Town segment.