Gummiel’s pretty much listed all the day related things. There aren’t any time limits or things you’ll miss if you’re too slow, although if you stay awake too long (3 AM), you’ll pass out and wake up back home.
There’s also 2 NPCs who won’t be available until day 10 (I think) who live on the west side of Port Beren - although I’ll be making things like that a bit clearer soon.