Each store has a different time they open and close. The hours get shorter each time you upgrade. Once you get Nookington's, sometimes Nook will ask you about the store. These are the options he gives you and what he downgrades to according to your answer:
Variety: Nookington's
Balance: Nookway
More Hours: Nook n' Go
Not Much: Nook's Cranny
If you don't like your current Nook n' Go store, just wait a while and he'll give you the options again.