Yes they do if you go to costco travel and enter a city you can choose a hotel with or without airfare. The hotel is not always in the city you request sometimes just close by. I suggest Google searching hotels where you want to stay to get an idea of pricing and location then compare with costcos prices and distance before booking.
Yes they have hotels that they are partnered with and offer discounts
Nope
Thanks! Your answer is awaiting moderation.