If you think the shortest distance between two points is a straight line, you might want to think again. I went on CBS Saturday Morning to share some little known—and in some cases, unpublished—ways to get to your destination using extended layovers. These routes are often cheaper, less crowded, and sometimes they even mean you get a bonus vacation. They’re called stopover flights. The trick to taking advantage of unconventional routes involves a little thinking outside the box. In some cases, it means picking airlines you probably haven’t flown before. Occasionally, especially in the United States, it could mean taking the train.

Stopover in Reykjavik, Iceland

Image Credit: Andreas Tille

If you’re like me, you did this stop when you were in college (and many college kids still do this) by flying Icelandair. With a one-hour change of planes in Reykjavik before heading to London or Paris, this option is a lot cheaper than most other airlines.

But these days, the options have expanded, and often they come with a big bonus. Looking for a route from the U.S. to Germany…or London, Denmark, maybe Sweden? Don’t fly nonstop. Instead, take Icelandair from a host of American cities—Seattle, New York, Boston, Washington, D.C., Denver, Minneapolis—and the airline will throw in a free seven-day layover that includes a two-night hotel stay in Reykjavik without additional airfare. Once you’re in Iceland, you can hike glaciers, go to the geothermal baths at the blue lagoon, and eat enough hákarl to satisfy you for a lifetime. Total price for the airfare and two nights in Iceland is $1205, which is comparable to most direct round-trip flights to any location in Europe.

A little note about Icelandair: they have a lot of flights that all stop in Iceland en route to Europe. That means that you have many more options than you might think. As a result, there are now more flights from Iceland to the U.S. than all other Scandinavian airlines combined.

Stopover in Panama

Looking to vacation in the Caribbean? If you fly on Copa Airlines (let’s say Los Angeles to Jamaica, for example), then you ask for the free stopover…in Panama. With no extra charge, you can visit two destinations. Now, with the 100th anniversary of the Panama Canal, the timing couldn’t be better. The Panama stopover only applies the moment you purchase the ticket, so just request the stopover while talking to the airline representative and you’ll be good to go.

Stopover in Istanbul, Turkey

These days, a round trip ticket from the U.S. to London can be very expensive. So, why not check out two great European cities for the price of one? It’s a bit counterintuitive, but if you fly through Istanbul, this can actually be accomplished. It may not make sense after looking at a map, but it does make sense in your wallet, not to mention the bonus—you get to see Istanbul. Fly on Turkish Airways (which happens to fly to more international destinations these days than any other airline in the world) and the airline throws in a free stopover in Istanbul that includes two nights at a hotel if there are more than ten hours between your connecting flights. Avoid the madness of trying to find a 10-hour stopover online by just calling the airline. They’ll be happy to accommodate.

Stopover in Doha, Qatar

Image Credit: Reid Nathan

If you fly Qatar Airways to any destination in the world, it will absolutely include a stop in Doha. Let’s say you want to fly from Philadelphia to Mumbai on Qatar Airways. The airline will entice you with a free hotel in Doha and a city tour. It’s an impressive deal called the Qatar Stopover Package, and it’s applicable for a party as big as nine travelers. For most Americans, Qatar is not a destination often considered, but look at the Qatar Airways route system, and you’ll notice that they fly just about everywhere. New York to Bangkok? Stop in Doha. Washington, D.C. to the Maldives? Stop in Doha. It’s truly a full-coverage system.

Amtrak: 15 Day Rail Pass

Finally, back here in the U.S., there’s a great stopover deal and it doesn’t involve flying anywhere. It’s on Amtrak, and it’s a program that does not get enough promotion. You’ll want to ask for it because it’s tough to find on the website.

The deal is called a 15-day rail pass, and once you get the pass, you have 180 days to use it! This is great for families. The pass gives you four one-way trips between two cities, and to all cities in between, over the same route. What this means is the pass is good for eight segments (a segment is any time you get on or off the train). The price? $449. Want a 30-day pass with 12 segments? $679. How about a 45-day pass with 18 segments? $879.

There’s a price for kids ages 2 to 12 as well, and it’s less than half the price of an adult pass. This deal is great on a number of different levels. First, if you plan right, you could save on hotels by sleeping on the train. Of course, if you do a fare comparison with flight routes, it’s a no-brainer. The cost of the shuttle flights between New York and Washington can be as high as $300 each way.

Want to travel from Seattle, Washington to San Diego, California? You can use the 15-day rail pass and stop in cities like Portland, San Francisco, Santa Barbara, and Los Angeles. You just have to use the pass within 180 days.

So, if you are flying abroad, don’t forget about the stopover deals offered by up-and-coming foreign airlines. They’re hungry for your business and they have the perks to prove it. Back home? You might just want to skip the flights altogether and travel the country in 19th century style.

Want to learn more about out-of-the-way destinations? Check out:

• 6 Offbeat Alternatives to Popular Destinations
• Escape the City With These Affordable Road Trips
• The Best Places to Visit in the U.S. on a Budget

By Peter Greenberg for PeterGreenberg.com