A version of Location Doubling that isn't about saving money: The story is set in the past, and the place where it's set no longer looks right, so it has to be filmed somewhere different that does look right. For the medieval look, this often involves hauling off to Eastern Europe. Hungary and The Czech Republic are common locations.
(Despite the trope name, examples where filming was done in a different part of the same country also count. The motive for the change of location is the key thing.)
Les Miserables, the 1998 film with Liam Neeson: Set in 19th-century France, filmed in the Czech Republic.
Cold Mountain: Set in America during the Civil War, filmed in Romania.
For The Babe, a biopic of Babe Ruth starring John Goodman, all the shots in Yankee Stadium were made at Wrigley Field (home of the Chicago Cubs) because it looked more like Yankee Stadium looked in the twenties than then-current Yankee Stadium did.
The 1955 film adaptation of Oklahoma was filmed in Arizona because modern Oklahoma was too heavily farmed and developed.
Amadeus, the 1984 film adaptation: set in 18th-century Vienna, filmed in the Czech Republic.
The Illusionist: Set in 19th-century Austria, filmed in the Czech Republic.
Ravenous: Set in 19th-century California, filmed in the Czech Republic.
A Knights Tale, set in medieval Europe (mainly France), was filmed in the Czech Republic.
The Holy City of Kairouan in Tunisia was the Raiders Of The Lost Ark filming location for Cairo. Appropriately the town's name means "little Cairo". For filming the scenes on Sallah's terrace, 350 television antennas had to be removed from local buildings to present a 1930s skyline.
Many Russian historical movies set in Moscow couldn't be filmed in the very Soviet, concrete, metropolitan Moscow. Movies about Imperial Russia or Early Soviet period are usually filmed in the older districts of St. Petersburg, and Muscovite Russia (as in Ivan Vasilievich) in one of the ancient Golden Ring towns.
Cadfael: Set in medieval England, filmed in Hungary.
Although Doctor Who is made in Cardiff now, the first story actually set in Cardiff was filmed in Swansea for this reason.
Doctor Who again: "The Vampires of Venice" and "Vincent and the Doctor", set in 16th-century Venice and 19th-century France, were filmed back-to-back in Croatia.
Robin Hood: Set in medieval England, filmed in Hungary.
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