The league is an obsolete unit of measurement that was once quite popular in many countries and remains popular in fantasy literature, which makes it eminently qualified to be used in fantasy role-playing. A league is simply 3 miles (or approximately 4.8 km), and its origin was practical: it was the average distance a person or horse could walk in one hour. If ever there was a unit of measurement made for itinerant adventurers, the league is it. And unlike the mile, it doesn't evoke a specific empire or culture. The league is both generic and folkloric. In other words, it is perfect for our uses.
1 league = 3 miles = 15,840 feet = 5,280 yards = 4.827 km
As for how many cubits are in a league...
1 league = 10,560 cubits
Whilst I'm on the subject, if you happen to be playing in an historical setting (or an alternate history) that uses miles and cubits, the following conversion may be useful:
1 standard mile = 3,520 cubits
Another option is simply to use all Roman units of measurement including those that survived to the present in some nations, e.g. pes (foot), mille passuum (mile), uncia (ounce), libra (pound), etc. (See the Wikipedia article Ancient Roman Units of Measurement for more information.)