I love to play around 1Pm, thats when all of the stores are open and you can get emotes from Shrunk! I can just get my daily chores banged out in 30minutes instead of having to go on multiple times.
My favourite times to play are : 1am until 7am - I don't like the 7am music at all so sound goes off then if I'm playing. 10am for all the shops being open, though again I don't like the music at all. And from 4pm on for the change of fish and bugs available, the changing light as it gets closer to sunset.