I believe the best calendar would be "World Season Calendar" made by Isaac Asimov.
The year is divided into four seasons of 13 weeks each.
A season has 91 days, so it's very convenient and has no months.
A week has 7 days, just like our Gregorian calendar.
The seasons of the year are named A -Winter, B-Spring, C-Summer, and D-Autumn in the Northern Hemisphere.
Example: December 1 in Gregorian calendar would be D-73 in World Season Calendar (WSC).
December 21, which is on or near the time of the northern winter solstice on the Gregorian calendar, is called A-01 on the World Season Calendar.
Since each of the four seasons contains 91 days, there are 91 × 4 = 364 days in all four seasons. To make 365 days, an extra day called Year Day is added at the end of season D. Year Day is day D-92, and is not assigned a day of the week.
During leap year, an extra day called Leap Day is added at the end of season B. Leap Day, when it occurs, is day B-92, and is not assigned a day of the week.
References: http://calendars.wikia.com/wiki/World_Season_Calendar