International Travel Issues As A Felon?

I'm a felon living in the U.S. I'll likely have international travel coming up for work. I want to know which countries will grant me entry and which countries won't. My employer is aware of my conviction and we discussed the conviction at length before I was hired. I passed all official screening. My felony is not drug related and I've obtained a U.S. Passport since my felony conviction. The conviction was ~4 years ago.

This is a large organization. I passed all screening, which is a box that is ticked at a corporate level. It's unlikely that anyone outside of HR knows about my charge. So my manager would be directing travel without knowledge of my potential "obstacle".

Obviously I want to avoid getting to a country and being denied entry. Where would I start if I wanted to...

1. Get a list of countries that would permit my entry.
2. Get a list of countries that would NOT permit my entry.

I have the impression I'll need to hire a lawyer of some sort to be positive about the accuracy of the work being done -- but what sort of lawyer? Do I need to find a lawyer that specializes in international law? I've never traveled internationally before either.