Whistler (About 1-1/2 hours north of Vanouver) has some great skiing too.
I grew up, on the weekends of my youth, in Summit County Colorado. My parents sold the cabin in Blue River (outside of Breckenridge in 1995. 
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Approx. an 1 1/2 - 1 3/4 hour drive from DIA via I-70, straight shot. Two hours from Colorado Springs via I-25 to C-470 to I-70 or via Highway 24 to Highway 9.
You have the choice of many ski “resorts” to choose from: Breckenridge (where parents had a condo and later a cabin,) Keystone and Vail in the same ski company if I remember correctly. Then you also have Copper Mtn. (between Frisco and Vail) and Arapahoe Basin. A Basin is extreme high country skiing so if you attempt it, do it on the last couple days of your trip when you would be used to the high altitude. But man, it is incredible with the views and the slopes. One of my favorite ski areas of them all.
But with Summit County you get free transportation (last I recall with the shuttle system, someone correct me if that’s changed) it’s a very family oriented community but does have things for the younger kids and for wild and crazy older singles like me. There’s an ice rink just outside of town, and they used to have Maggie (a little lake) open for ice skating in town. Food is excellent at most places and if you do have a hankering for a little shopping, there is an abundance of it. Breckenridge has done what it can to keep with that 1800s gold mining town but has had to bow to the commercial success, but it remains in my heart.
Now, Steamboat is a little more quaint. I have never skiied there so I don’t know the slopes but the town is mellow and even more family oriented if you are looking for a more mellow vacation. I have spent quite a bit of time up there because of my previous sales job.
It’s about 3 - 3 1/4 hours from DIA and 4 hours from Colorado Springs. If you go to Steamboat, rent an SUV because if you take the typical route, over Rabbit Ears Pass, it can be hairy and scary if it has had a lot of snow.
But it is a nice community with casual and nice restaurants and they do have a little more mellow night life that you could even take your kids to, in some places. This may be more what you are looking for but with Summit County you get five resorts to swoosh on.
Aspen and surrounding community is nice but WAY expensive and really, last time I was there, not a lot for kids to do, even for older teens of 18 or so. So I say that area is out unless you go in the summer.
If you are looking for complete kick back, I must admit I have never been to Red River, New Mexico, in the winter but I have been there in the summer and it’s family oriented like Steamboat. It used to be a big biker town but now it’s family all the way. I went there in the 90s for a family function and it was mellow and perfect.
Anyhow, I stress Colorado because I have lived here all my life. I think I have a pretty good feel for it and I do have contacts around both Summit County and in Steamboat Springs so don’t hesitate to email me if you want more information.
I need to clarify something.
Vail is in Eagle County and there is also Beaver Creek to ski. But Vail is only about a 1/2 hour from Breckenridge, does require your own transportation unless you catch a Greyhound. So, you have six resorts to choose from in the immediate area.
Vail is expensive to stay in, just a step down from Aspen. Breckenridge and Keystone are a step down from that, price wise. Keystone/Dillon is slightly more “remote” for lack of a better word, while Breck gives you more options if you stay in town.
Frisco is nice but it is not close in to a ski area, it is the center of action to all the resorts and tends to be less expensive. It too has nice restaurants, used to go to the Blue Spruce for steaks and play PacMan…hehe, what an odd memory.
Anyhow, I hope I have helped a bit.