When I buy an iPad at Costco, can I purchase Apple Care at the Apple Store?

Yes. You can purchase Apple Care+ within 60 days of original purchase of the iPad.

AppleCare+ - iPad - Apple

You do understand that a phone purchased at Costco will be locked to the first carrier it is used with, or to their "private" carrier? Costco does not sell unlocked phones. Unless the price is substantially lower than buying it directly from Apple it is not a good deal.

You should be able to buy it right there at Costco when you buy the device. Costco is an Apple Authorized seller and so should also be able to process your AppleCare+ purchase at the same time.

Sorry, I wasn't aware of that. Probably because you posted in the iPhone forum, not the iPad forum, so I assumed that you meant iPhone.

I've suggested to the hosts that they move your post.