score:1
Given your restrictions on transportation namely public transportation your choices are limited to:
All located in New York City.
Upvote:2
Six Flags Great Adventure is a very large amus*m*nt park and perhaps the most obvious choice. Google says it is 1:06 away from Union City by car. There are smaller parks closer to Union City which may be better for younger kids, e.g. Bowcraft. Your choice depends a bit on your group...