Agree with Salt Lake as a good choice. You've got several ski areas with great terrain at all levels, quite close to SLC.
Also agree with Keystone and the rest of Summit County Colorado as a good possibility. Breckenridge and Copper Mountain are also right here, and are other good choices. All those areas have good ski schools and have lesson-and-lift packages. Breck and Keystone are both owned by Vail Resorts so a multi-day ticket at either is also good for the other. Summit County is about 1.5 hours up the mountain from Denver International. And there's a totally free bus system throughout the County. You could get off the plane at DIA, get on the Colorado Mountain Express shuttle van to your destination in Summit County (Keystone, Dillon, Silverthorne, Frisco, Breckenridge, Copper Mountain) and never need a car the whole time. Staying in Dillon or Silverthorne (or to a lesser extent Frisco) will be a bit cheaper than staying in Breckenridge or on/near-mountain at Keystone, and you're still a quick Summit Stage free bus ride from any of the mountains. Staying in Breck puts you in a real "ski town" environment with lots of fun restaurants, theatre, music, bars, shopping etc.)
Have you been at altitude? SLC is at about 4000 feet and the base of the ski areas are at about 6400 around Park City (Canyons, Deer Valley, Park City Mountain Resort) and more like 8000 around Big and Little Cottonwood Canyons (Alta, Snowbird, Solitude, Brighton). Here in Summit County, the base areas are around 9300-9600 feet and the towns are at about 9000 elevation. Not a big deal if you make sure to drink plenty of water, avoid alcohol the first day or so, and don't try to go big your first day at altitude.
Skiing blues the first day after a 4 hour lesson? That's an aggressive goal and probably unrealistic and not what you want to aim for. Skiing confidently from the trails off the beginner area chairlift by the end of your first full-day lesson? That's a more realistic and enjoyable goal. A couple of days into it and you'll be able to share some of the same terrain that your wife would be enjoying. You'll have more fun if you approach learning to ski as "I want to learn to ski because my wife has sold me on how much fun it is" as opposed to "I need to ski terrain X by date Y".
(Truth in advertising: I teach beginners at Breck but I'm not pitching that area or myself specifically - we've got a boatload of very good instructors at all the Summit County areas, many of whom post here on EpicSki. Whether you go to Copper, Keystone, or Breck out here, you'll enjoy it)