Arguably the best order at the moment to get the fastest run would be as follows:

Tutorial, General Tiel, Azure Cove, Mines, Desert, Burial Grounds, King Lytherel, Vulhe Castle

Azure Cove is one of the easiest places to mess up a run, so getting it out of the way early is very helpful.

Mines is the obvious second spot, if not for the skip, then for the fact that you can unlock the guy who turns all of your items into permanent stat boosts.

As of right now, there is absolutely no reason to go to Burial Grounds before Desert, and if anything it can slow down your run by ~4:30, due to the fact that you get no stat benefit by clearing Burial Grounds before Desert. The enemies on Desert are still a bitch to kill.

Burial Grounds LAST, because it is the most linear of the four main locations. It is long (~10:00) and boring, but a great mental checkpoint time wise. Current WR pace is finishing it by ~42 minutes.