To identify National Park Mystery Spot 15 you were given this to work with:

Queeg or Bligh, standing high, after half a Roman century.

Countertop stuff that's tough enough.

A mailman hung out at Cheers,
Shooting the breeze and quaffing beers.

 
The answer is El Capitan in Yosemite National Park. Here is how you can work it out. Backwards actually works best. It also helps to know that Capitan means "Captain" in Spanish (and most other European languages).

One of the featured characters of the 1982-1983 television comedy series Cheers was Cliff Claven. Played by veteran actor John Ratzenberger, Cliff was the know-it-all mailman who "hung out at Cheers, shooting the breeze and quaffing beers." He appeared in 273 episodes.

"Countertop stuff that's tough enough" is an apt description for granite. El Capitan, a Yosemite signature landform of world renown, is a 3,000 foot-high granite cliff. That certainly qualifies it as a thing that is "standing high."

In Herman Wouk's 1951 novel The Caine Mutiny, and in the classic 1954 film of the same name, Lieutenant Commander Philip Francis Queeg, USN, is the fictional captain of the minesweeper USS Caine. Humphrey Bogart played Queeg in the film. British Royal Navy Vice Admiral William Bligh (1754-1817) was the captain of the HMS Bounty when it was famously taken over by mutineers in 1789. In the 1962 film classic Mutiny on the Bounty, Trevor Howard played Captain Bligh and Marlon Brando played lead mutineer Lieutenant Fletcher Christian.

Half a century is 50 years. The Roman numeral for 50 is L, which is pronounced "el". "After half a Roman century" is any term that follows "el".