I quite like the hobbit calendar. 12 months of 30 days each, plus 5 (or 6) extra days that don't belong to a month and are celebration days. Mid-year day and the leap day don't have a day of the week, so each date always is the same day of the week.
Even now 29 Feb shouldn't exist, it should just be "leap day" and have no numerical significance.
Screw the computers, they can learn to adapt.
Of course those days would be very hectic travel wise if the entire population of earth were to migrate around on those days.