How can I see all commercial destinations to a country from a particular airport?
There can be a number of websites which can provide this information. Wikipedia and the specific airline's website can be a great resource too.


OpenFlights gives you a graphical representation of direct flights from a particular airport. It appears that this service is for all major airports across the globe.
SkyScanner can provide the information you are looking for. As for your example, you'll enter Las Vegas in the From text area, and then leave the To area blank. It will search all destinations (grouped by countries) where there are direct flights (or with one stop) available.