Go to them.
My favorite way to travel is country-hopping to the different places my friends live in. From Asia to Europe, I've been country-hopping and living like a local. If your friend is living in a destination you're been dying to go to (or even one you aren't) I have one word for you: GO!
My favorite and most obvious reason for visiting your friends abroad is the opportunity to live the real life of the cities inhabitants. No tour busses, no scams, no looking like a tourist. Walk down the streets with your coffee-in-hand, no need to look at a map because you're simply strolling with your pal.
Save on lodging costs by crashing with your friend. Before you go, ask if you can make use of their kitchen when you're visiting to save on some meals. Now obviously, budget to eat out and try the local cuisine, but it helps the wallet to cook a few meals at your temporary home.
When your friend moves abroad, you may worry that you won't have anything in common anywhere. I've found that visiting my friends overseas bonds us even further because we are continuing to create new memories — not just talking about the past.
Your friend is living an entirely new life. That is brave. No matter how independent or outgoing they are, they are in a completely new element. Very few people back home will even have an inkling of an understanding of their new life. Now, when they refer to their favorite park or coffeeshop you actually know what they're talking about, and someone from their “past life” can actually relate to their experience.
If you're thinking of making the jump across the pond yourself, it's helpful to have seen someone you care about already do it. Consider it your trial one. Perhaps ask if you can visit your friend's work one day, learn the commuter system, etc. Things are a lot less scary once you see how attainable it is — and you know someone doing it!