Kuwait is a tiny country. It is so small that driving for two hours in any direction from the center of the city puts you in another country. There are 2.5 million people in Kuwait and only 1 million of them are Kuwaitis. The remainder are imported labor, just as you will be if you choose to work there. Most of the laborers brought into Kuwait, except for female house servants, are males from Egypt, India, Pakistan, Bangladesh, and the Philippines. One of the most serious and pressing public policy issues in Kuwait (and Saudi Arabia, where similar conditions exist) is the country's over dependence on foreign labor. Most Kuwaitis, especially if they have college degrees, hold out for government jobs, which are essentially lifetime appointments with generous retirement benefits. Very few opt to work in the private sector, where wages are depressed as a result of the importation of inexpensive labor.
Certain articles are proscribed within Kuwait, including pork and alcohol. And lest you think bringing in a bottle or two of spirits is inviting a jail term. if you are entering Kuwait for the first time, I would advise you not to attempt to bring any alcohol into the country. More pernicious than the banning of alcohol, however, is the censoring of books, magazines, and films. These are the least objectionable in terms of content to the censors. Love stories and anything remotely related to sex is heavily censored or banned. Same applies to videos, though the music market seems to be a little bit more open. Print material is also censored for both graphic and editorial content. Pictures of women in swimsuits and low cut blouses, for example, are routinely marked over with the censor's black marker, as are articles, quotes or comments deemed politically or religiously offensive.
So, what is there to do in Kuwait? There isn't much- Shopping is also a favorite activity of the Kuwaitis, though you probably won't be interested in traveling halfway around the world to blow your salary on consumer goods. But if you want it, they have it. There are several upscale shopping malls, and the Salmiya high street features such shops.
The Friday market is a huge weekly open air market that is always fun to visit if for no other reason than to take in the sights. You'll find almost everything imaginable on sale here, including livestock, Persian rugs, antiques, furniture, household items (such as laundry detergent, kitchen ware, and other daily necessities), clothing, and just plain old junk that someone carted out of their garage, storage shed, or basement.
Gold is also a big item in the Gulf and there is plenty to be had in Kuwait. Most of the jewelry is imported from India and given the cheaper labor costs there you probably do save a little on labor and spend a greater proportion on the gold itself.
Driving around in your car is another favorite pastime of the Kuwaitis, especially the young. If you're going to participate, a cell phone is de rigor.
Outside of restaurants and coffee shops, there are very few places for informal social gatherings. There are no bars, discos, or music clubs. Many of the large hotels attempt to fill this gap with seasonal events such as bazaars, or weekly musical performances by local musicians.
With no bars or restaurants available for socializing, many expats become part of social circles that hold weekly gatherings, the meetings rotating amongst a circle of friends.

As the rules are changing very often, please check with the officials for latest rules and procedures.