You can go to any zone at any level if you can survive the aggro. But at level 20 (and before) you should be able to solo in Thundering Steppes and Nektulos which are outside of Antonica and Commonlands.
I don't see why you would have a problem going anywhere else as long as you can survive the trip. Its not like you can get to areas outside of Freeport/Qeynos without getting to a ferry bell that takes you to the other continent. There are plenty of evil/good players on both continents.
I would recommend you get to level 10 before you attempt the journey so you don't have to return until level 19 to do your subclass quest. But that's not a problem either since its rather easy to get around in EQ2.