Trap/Skeet can be an excellent way to get a woman into shooting. It has kind of a golf-ish or bowling-like connotation about it, especially in amatuer ATA leauges, and women seem to be better represented in sporting clays than some of the other shooting environments. Look in the yellow pages for gun clubs or shooting clubs. If you can't find any, ask your local gunshops you frequent if they know of any.
Very often, a skeet/trap club is really little more than a golf "driving range" but for the shotgun/clay sports, and open to the public. Becoming a member of the club is often only required to participate in leauges, and gets you $1 off the price of a round, so it's a good deal if you plan on going frequently but not required.
Some clubs may be very expensive and exclusive, or have manditory membership, but there should be a open-to-public club/range in your area. The short range of shotguns, and the fact that it seems to be one of the more "PC" shooting sports, means shotgun clubs can often be found closer into the suburban areas of a city than outdoor rifle ranges are.
Ask if anyone would be availible to give an impromptu lesson, or if they have a "lesson leauge" etc. at the club. Very often one of the owners, a manager or a resident "pro" will run a class session for new shooters, or even experienced ones looking to improve. Also ask if the club has rental guns, you may want to start your wife out on a 20ga if you're worried she's recoil sensitive, and a gas-semi like a Baretta 390 or a Rem 1100 would suck up some more recoil, a semi would also be handy if she wants to try doubles, where shucking a pump fast enough might be troublesome. The Federal bulk-packs of 100 rounds for $15 that Wal-Mart carries in 12 and 20ga are cheap, and also pretty soft shooting.
The only other thing I could add is you might want to try your wife on a .22 LR rifle first, as alone and away from other shooters, and gunfire noise as possible. Being in any kind of structured setting where you have other shooters, range commands, trap/skeet/station change commands, and shooting in close proximity can be intimidating. If you think shotgun is the only thing she'll try, see if you can go on a slow weekday evening, like a Tuesday or Wednesday, and ask if you can get an empty station at the shotgun club, or a familiarization walk-through.
