The best season to visit Romania is the Holiday Winter (for Christmas and New Year holiday). This is the best season in my opinion because we have a lot of traditions especially for Christmas, and you'll be very surprised by the guest's hospitality, especially in the rural places like Maramures, Bucovina, or Transilvania- Brasov, Sibiu county. In Brasov county for exemple is a tradition for Christmas where 2 groups of young men called "Feciorii" go and sing Christmas Carols all day for every house they see and where they see girls in a house they get them and try to convince them to join them later on the Christmas Ballroom to dance and cheer.
For others who like hiking or trekking the best season is the midst of Spring, because you can see the real nature with all the beautiful mountains, great woods, and caves like Bear's Cave or Bat's Cave.