Traveling internationally isn't cheap. With increasing airline, hotel, food and souvenir prices, your vacation budget can disappear faster than you can say "duty free."

But don't forget about that one expense international travelers have to pay before they even start spending -- the foreign currency exchange fee.

Exchanging U.S. dollars for international currency can be expensive. Unofficial exchange places, like local kiosks at the airport, are notorious for their expensive mark-up fees on foreign currency exchanges.

By far, the cheapest way to spend money overseas is by using credit cards. 

Most cards charge a 1% to 3% fee for every international transaction, which can really add up quickly.

Smarter Travel estimates a week-long European vacation for two will cost a minimum of $2,000 (not including airfare). With a 3% charge for every purchase, that adds up to an additional $60 in fees alone -- just to spend your own money.

Fortunately, there is a growing list of credit cards that don't charge foreign transaction fees. Some will even let you earn travel rewards that can go toward your next trip.

But First: Visa, Mastercard, AMEX or Discover?

Not all credit cards are accepted abroad -- even if you don't have the PERFECT card, at least make sure you have one that will be accepted in the country you're going to.

For the most part, Visa (NYSE: V) and MasterCard (NYSE: MA) are both widely accepted (Visa slightly more so) worldwide. American Express (NYSE: AXP) and Discover (NYSE: DFS) are also gaining popularity, but won't work in every country. 

Even if you have multiple cards, be sure Visa is one of them and you should be fine almost anywhere credit cards are accepted.

Travel Card Must #1: A Card With Rewards

Points, miles, gift cards, cash -- it seems like there are almost as many different reward programs as there are credit cards.

For me, nothing beats cash, so I tend to gravitate toward cards that offer cash back. But there are a number of cards that offer other travel-friendly incentives, like airline miles and free hotel stays. 

These can be great for frequent travelers since most travel-specific reward cards give large bonuses to new cardholders and double or even triple points for every dollar spent on travel expenses.

While rewards make are nice perk, there's a more important aspect you need to look for when searching for your ideal travel card...

[Some cards even offer 3% to 5% cash back -- See our list of the 5 Highest-Rewarding Credit Cards on the Market]

Thankfully, these cards do exist -- but some come with an annual fee. 

These annual fees can run from $50 to more than $450, which just goes to show that it pays to read the fine print.

Typically, cards with higher annual fees offer better perks, like concierge services, higher mileage rewards and more cash-back.

With fees and rewards in mind, here are some of the best picks for international travel credit cards.

Chase Sapphire Preferred

With no foreign transaction fees and double points for all travel and dining purchases, the Chase Sapphire Preferred card is meant for travelers. Even when you're not using it to buy train tickets or pay for dinner, you still earn one point for each dollar spent.

Chase (NYSE: JPM) offers a special deal for new Sapphire Preferred cardholders: Spend more than $3,000 in your first three months you'll score 50,000 bonus points -- good for a free international flight on most carriers. The card even allows you to transfer earned points to participating frequent traveler programs without penalty.

PROS: No foreign transaction fees, double points for travel/dining, flexible rewards, no limit on points earned, points never expire

CONS: $95 annual fee after the first year

[InvestingAnswers Feature: Credit or Debit? Your Choice Could Cost You 3%]

Capital One Venture Rewards

Another great choice is the Venture Rewards card from Capital One (NYSE: COF), which is my (and Alec Baldwin's) favorite credit card for travel. 

Like the Chase Sapphire Preferred card, this card has no foreign transaction fees. Unlike Chase Sapphire, the Venture Rewards card offers double miles on every purchase (which can be redeemed for any travel expense, not just flights).

This card also comes with a new account perk: Spend $1,000 during the first three months and earn 10,000 bonus miles. 

The one downside to this very rewarding card is the $59 annual fee you have to pay after the first year. Not bad, depending on how much you spend annually... BUT there's a similar card that gets around this...

PROS: No foreign transaction fees, double miles on every purchase, no limit on miles earned, miles never expire

CONS: $59 annual fee after first year

Capital One VentureOne Rewards

Meet the VentureOne Rewards card. This lesser-known card comes with many of the same benefits as the Venture Rewards card (including no foreign transaction fees), but without the annual fee. 

It earns 1.25 miles per every dollar -- only slightly less than the aforementioned Venture Rewards card -- and comes with the same "spend $1,000, earn 10,000 bonus miles" deal for opening an account.

This card is a great option for smaller spenders interested in the Venture Rewards card -- you get many of the same benefits and never have to worry about purchasing enough to make the annual fee worthwhile. 

PROS: No foreign transaction fees, no annual fee, no limit on miles earned, miles never expire

CONS: Earns fewer miles per dollar spent than the Capital One Venture Rewards card

[Ready to travel the world with your new cards? See our list of The 5 Best Places in the World to Retire]

The Investing Answer: If you want to save money on overseas credit card spending and don't spend a lot of money, the Capital One VentureOne Rewards makes a well balanced travel card. If you're a bigger spender and want a card that gives you the most miles for your purchases, the Venture Rewards card is the best card for travel. If you are looking for flexible rewards, for everything from cash to travel, then Chase Sapphire Preferred is the best card for you.