Daily Routine:

* You can get an avatar from the ones marked with a star (*).

Every day you should visit these places (for free):
Tyrannian Omelette
Giant Jelly
Healing Springs - every hour
Fruit Machine
Coltzan's Shrine - every 12 hours
Tombola
Turmaculus * - when awake (Check out time predictions)
Snowager * - when asleep (3 times a day)
Bank - to collect interest
Secret Laboratory * (if you have the map)
Petpet Laboratory * (if you have the Lab Ray and the map)
News - for updates

And these you have to pay for but are (some) worth it:
Wheel of Excitement * - every 2 hours
Wheel of Mediocrity * - every hour
Wheel of Knowledge * - every 24 hours
Wheel of Misfortune * - every 2 hours
Wheel of Monotony * - every 24 hours (takes forever)
Scratchcard Kiosk * - every 6 hours (time limit includes all kiosks)
Haunted Scratchcard Kiosk * - every 6 hours
Lost Desert Scratchcard Kiosk - every 4 hours
Buried Treasure * - every 3 hours
The Kadoatery * - check out the boards for re-feed times

In December: Advent Calendar (sometimes *)