North to South because the air would go from colder to warmer rather than from warm air to colder air if done in the opposite direction and the reasons for a diagonal course is because it would cover a lot more 'interesting sights to see from the air' for a multi-day 'air cruise' type cruise (best way to explain that is a literal air-cruise as in a sea-cruise).
For a passenger trip it would have to be an extremely HNV costing (passenger cost/ticket price paid * weight able to be carried) but do-able for say 4 - 7 passengers but Cargo would be the way to go for the bread-and-butter stuff because A) The weights and destinations are pre-known and optimised and B) Going on a diagonal route would beat road and rail delivery speeds and provide some financing to the back-haul of getting the (now empty) air-ships back to the departure point.
[Edit To Update]: Ughh! you can tell I'm not a pilot because cold air is better than hot air in terms of aircraft lifting capacities so South to North would be better and maybe a change of route from Miami to Seattle would also work out ok in terms of shipping ports that intersect with cruise ship ports.
[Double Edit, Sorry]: On second thoughts, North to South for passengers and South To North for cargo is better because cargo is low margin so would need the greater lifting capacity. Or not.... Like I said, pure spit-balling!