Well, first thing I do every morning is check the shops. When I was trying to upgrade the shops I'd buy everything in each of them. I don't do that now as all mine are upgrades but if yours aren't? I'd add it to your daily list.
Check every rock, eventually you'll remember which rocks are permanent in your town so it will be easier to spot which Rock has an ore inside.
There will be one ore rock and one money rock daily.
Shake every tree (except fruit unless you want to). There will be 2 pieces of furniture daily from the trees and the rest of them will have money or bees nests come out if them.
Generally there's about 3 or 4 fossils spawning daily. Be sure to just dig randomly behind buildings even if you can't see what you're doing as they do spawn there too.
Also, if you're wanting to get the pascal furniture, be sure to go diving for a scallop once a day and you should obtain the full set I no time
Don't think I've missed anything....
- - - Post Merge - - -
Oh you will also want to water any flowers you have and check for weeds. There will be about 3 or so weeds to pull daily.
Unless of course you turn on beautiful town ordinance, in which case there will be fewer weeds and watering your flowers won't be necessary