TMNT outside New York in the 1987 cartoon.
 

In the 1987 TMNT cartoon, it wasn't often the TMNT left New York City. It would have been fun if they travelled more around the Earth, like Archie Comics, and had to hide on aeroplanes. They never visited present Japan.

This is what I remember of the TMNT outside New York City in the 1987 series:
Arctic Ocean Ice Cap and underwater ("season 5-7, when the Technodrome was there)
Europe ("Vacation in Europe series")
Leonardo in a small town ("Unidentified Flying Leonardo")
Mount Rushmore ("The Big" trilogy)
Niagara Falls ("Return of the Technodrome")

They went to plenty of places. Mostly when they went on a whirlwind tour of Europe in the 1993 Season or whenever they were on TV between 1991-1993:

Dublin, Ireland
Amsterdam, Holland
Lisbon, Portugal
London, England
The Alps
Paris, France
Venice, Italy
And usually, when the turtles are in a contryside setting or empty area, they are on outskirts or outside New York nearby. That does suck, they never ended up going to modern Japan, but there was "Legend of Koji" where they go to 16th century Japan which defines their heritage they were brought into by Splinter and lifestyle..sort of. I would like to have known what Splinter thinks about modern Japan compared to his completely different upbringing, with the fast food culture. I bet you Michaleangelo would've really digged the video games and cartoons. Possible Mikey reaction "WOOOH! MONDO BODACIOUS MANGA!!

TMNT on travels.
 

Forgot to mention that Shredder returned to modern Japan in "My Brother, the Bad Guy" in the 1987 TMNT cartoon. And the TMNT and Shredder were sometimes nearby New York City, like the amusement park in "It Came from Beneath the Sewers"

This is where the "Vacation in Europe" series take place (sometimes the episodes take place in the countryside and suburbs around and outside the towns and cities I mention here).

"Tower of Power" = Paris, France
"Rust Never Sleeps" = Paris, France
"A Real Snow Job" = Alps, Austria
"Venice on the Half-Shell" = Venice, Italy
"Artless" = Florence and Rome, Italy
"Ring of Fire" = Lisbon, Portugal
"The Irish Jig Is Up" = Dublin, Republic of Ireland
"Shredder's New Sword" = London, UK
"The Lost Queen of Atlantis" = Athens, Greece
"Turtles on the Orient Express" = Orient Express (France, Germany, Austria, Hungary, Romania)
"April Gets in Dutch" = Amsterdam, Netherlands
"Northern Lights Out" = Oslo, Norway
"Elementary, My Dear Turtle" = London, UK. Includes a time travel back to 1890 London.

just the mention of these european episodes is making me feel exicted all over again. I can't wait till we get this far into the dvds where we get to these episodes. And this was really a great arc in the seris, I really enjoyed it. It started off season seven really nicely.

Also I believe the turtles went to Florida on more than one occasion where Leather and the frogs live.