St. James is a great location and on any other mountain it would be considered deluxe. At Beaver Creek, it's mid-level quality compared to the surrounding hotels/condos. So, what you get is a very good place to stay at a great value (relatively speaking) in a great location in the village. The Dusty Boot is a terrific restaurant (with pretty good margarita's too)located in St. James. Again, a decent value relatively speaking. A very good cheap restaurant is Pazzo's Pizzaria in Avon, just outside of Beaver Creek.
There are ample discussions of where to ski at Beaver Creek on this site so, I'll focus on the non-skiing tips. If you want to check out where to ski, just do a search using the word "Harrier". Any decent review of Beaver Creek skiing always includes that run as being great (which it is IMHO).
If you rent a car (which is probably not much more expensive than paying round trip fare to CME to get your whole family back and forth to the airport), make sure you get to Vail for a day or two of skiing and dining as well. Adventure Ridge at Vail is great for the family at night. Another option is snowmobiling for a half day if you need a break from skiing. Nova Guides did a great job on one of our trips. I'm not sure what the conditions would be like for snowmobiling in April.
Just hanging out by the fire pit in front of the Hyatt is fun at night. Go inside the Hyatt, grab a couple of warm drinks and then go out sit by the fire.
If your kids are youngish, there's a great indoor pool with a great water slide at the Avon Recreation Center. Another great after ski activity.
Movie theaters are located in Edwards just down the road, where there are also some pretty good restaurants.
Feel free to PM me if you have any questions.