Here are the chores presented in the game so far (that I have seen, anyways). After the second update, they will tell you which floor you need to go to.
~ First (June) Update ~
Straighten paintings
Pick up banana peels
Collect snails
Pick white flowers
Turn off showers
Pick up dirty socks
~ Second (July) Update ~
Turn off fans
Clean sign
Chase moths out of Wardrobe Room
~ Third (August) Update ~
Turn off sprinklers
Check mail
Feed the unicorns
Feed the Extremeasaur
Clean the bottom of the pool
Feed Cyrus the Sea Monster
Clean birdbaths
Clean up Bloo's graffiti
Make the beds
~ Fourth (October) Update ~
Polish fake tombstones
Light jack-'o-lanterns
Collect trick-or-treat candy by main door
Manicure zombies' hands
Pick up plastic skulls
Patch pipes in basement
~ Fifth (November) Update ~
Feed the turkeys
Raise the anchor on the Mayflower
Pick up dead leaves
Inflate Pilgrim balloons
Create corn husk dolls
Pick up Pilgrim hats
Mail out Creator Reunion Party invitations
~ Sixth (December) Update ~
Light the Christmas tree
Warm up the snowmen in the yard
Fill Stockings
Light up Christmas decorations on porch
Clean (snow off of) sign
~ Seventh (January) Update ~
Water flowers
Put blankets on unicorns
~ Eighth (February) Update ~
Blow up heart balloons