I'm a firm believer in placing recent weather events high on the list of factors for a question like this. Rather than picking a mountain this far in advance, I would wait and make the decision last minute. Really, any of these mountains offer something fun, however the snow quality/quantity can push any one option over the top. Remember, there are almost a dozen mountains within an hour of the airport, however the snow totals vary quite a bit depending on from which direction the storm arrives.
If you are spending the bulk of your time in LCC, I assume you are staying in SLC or LCC? If that's the case, you probably have transportation already lined up? Follow the weather the days before your free day and if you're lucky enough to have a storm, head to whatever mountain is reporting the best snow.
There's a lot of opinions on what is the best mountain, but honestly they are all pretty good for their own reasons, especially if you are there for only a day. So if you experience a Utah storm, I feel the question should be "where's the best snow" instead of "where's the best mountain."