Mailbox, Nook, Listen for the birdie, if birdie, check bulletin, if no birdie, I go straight from Nook's to the Able Sister. (I go, regardless if there is a birdie, or if there isn't a birdie.)
Usually, I go to check my Mail first of all (if I have any). Otherwise, I'd check my inventory, and depending in what's in my pockets I'll go fish and sell, or go spruce up my house.