Does one need to be a U.S. citizen to fly and visit foreign countries, such as Russia?

Question

Or can permanent residents vacation in foreign countries, too?

Answer 1

Here is the info you need from the state. The website also lets you know other things permanent residence can do.. Congratulations!

International Travel
A Permanent Resident of the United States can travel freely outside of the US. A passport from the country of citizenship is normally all that is needed. To reenter the US a Permanent Resident normally needs to present the green card (Permanent Resident Card, Form I-551) for readmission. A reentry permit is needed for reentry for trips greater than one year but less than two years in duration.

Answer 2

Permanente Residents of the US can travel anywhere they want as long as they have their green card to allow them back into the country - also, everyone, no matter what your citizenship is, must travel with a passport now.