If you just restarted your island you won't be able to unlock cooking right off the bat. You need to wait until your Resident Services is built into a proper building and you also need to have a 3 star rating in order to unlock cooking.
Yeah, the Kapp'n tours, Harv's Island stalls, and most of the Nook Stop options were locked behind the 3 star island/KK concert for me. It made me progress my game a little faster than I had intended because I was anxious to go on tours.