International law is extremely interesting compared to many other aspects of legal practice. But you have to understand a few points before you commit to such practice:

1.) You are likely to find such work mostly in major cities. If you are in America, Washington, DC, New York, San Francisco, Los Angeles, and a few others cities, mostly on the coasts will dominate practices with international base.

2.) You are likely to find such work mostly at large firms. I'm sure there are boutique law firms that specialize in aspects of international law but these likely composed of highly experienced attorneys who would not take on lawyers right out of law school.

3.) You will need to specialize in an area that has an international law clientele or international law component, but unless you are an academic, international law is a not a practice area. Most lawyers who would categorize themselves as international lawyers are specialists in an area that has international clients.

4.) You will likely need to travel a great deal. I assume that part of your interest in international law relates to a desire to travel. So, I'm sure this is fine.

Is it a good career path? Leaving aside whether being a lawyer is a good career path, if you want to work in a major city, are fine working in large firms or organizations, and have a speciality in mind, international legal practice is fascinating.