I really like the peaceful early mornings, around 7AM. Only thing I don't like is that the shops aren't open yet and most villagers still asleep. It's nice to work in your town though, arrange flowers, clean up your house, etc. I also like around 5/6PM when the sun is setting.
I really like sunset around 5:30-6:30pm the most. the colors are just incredible at those times. I also enjoy 8am-10am since it's just so bright and cheery but I also like late night like 12am and 1am. I really want to see sunrise at some point but haven't gotten around to it yet. It depends on the season, honestly.