Kuwait is really Kuwait City, there seems to be very little to see outside the capital, and no way of getting there short of hiring a car, so Kuwait City it is then (although the airport is very nice, it has a Debenhams, and a Pizza Express!)
When I was in Kuwait it was celebrating Independence day, and Liberation Day - two back to back holidays, the disadvantage of this was a number of the things I'd like to have seen where shut. This was compounded with the last few days of the 40 days of mourning due to the death of the Emir - Oh Well. However the Aquarium was open, although the definition of aquarium must be quite wide in Kuwait, with exhibits of Scorpions, Owls, Hedgehogs and even Bats (as well as all the standard fishy type things!)
Probably the highlight of a trip to Kuwait has to be a visit to the Kuwait Towers, a series of spikes with balls impaled on them! The have been part of the Kuwait landscape since 1979, and are still standing despite the attention of the Iraqi invaders. I took the lift up to the viewing platform 140m above the ground. The views of Kuwait city from the top are amazing, but you also get a better view of the covering of the towers, which are a series of ceramic disks.
One of the most amazing "finds" in Kuwait, was the "lost and found" board in the main bus station, this was a free standing display case, with id cards, credit card, passports, even a bank savings book on display waiting collection by their forgetful owners.
While wandering around the souq, I found a money changer with the tools of his trade on display in a glass case; wads of US Dollars, next to Chinese Renminbi and crisp new 50 Euro notes. All just sitting there for all to see!
I'd be lying if I said that Kuwait has an active tourist industry.