West Coast is huge, I can only assume you mean from Las Vegas.
Miami is probably your best bet, as they have 3 flights a day. Hard part is arriving early enough to meet a connection to GT-you may have to overnight in Provo.
There are numerous daily flights from Provo to GT, with the last one being around 5:30 pm.
Since you've never been, I highly suggest after your overnight having a later connecting flight, so you can lay eyes on that gorgeous Grace Bay Beach.
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