One specific recommendation for: (not in Silverthorne but close)
Precision Ski in Frisco. One stop (couple of miles) west on I-70, where you'd be getting off for Breck on Hwy 9 in Frisco anyway, or passing nearby if you're going to Copper. Only about 1/4 mile down the road in a strip mall on the left just past the Messianic Jews for Jesus A&W.
There are other good shops around, but Precision tends to be the local's choice for work.
In Silverthorne itself you tend to have more of the ski-resort-owned small chain stores such as Mountain Sports Outlet (owned by Vail) and Pure (owned by Intrawest). Not that there's anything wrong with that. But I like the feel at Precision, they listen to what you want (especially on tunes but I'd trust them on other work based on that experience.) You can probably get a good mounting at any of them.
One specific recommendation against: (not in Silverthorne, but I assume you might be heading to Breck at some point and might consider a shop there)
Unfortunately I do not recommend Norway Haus in Breck for mounting. Like them for some soft goods sales, and it's where a great bootfitter runs an independent practice in space he rents from them. But I wouldn't bring a pair of skis that I bought elsewhere to them for mounting (Yes, I did that once). Unless they happened to carry that same model and length.