I've stayed at this Holiday Inn Express and Suites in Carlstadt, NJ, more than once. It is not near a train station, but it is about a five-minute walk from the bus stops with frequent service to/from the Port Authority Bus Terminal (which is closer to the Broadway theaters than Penn Station is).

https://www.ihg.com/holidayinnexpres...X-_-US-_-CSTNJ

There's also a Hampton Inn across the street from the HI Express.

The bus to/from runs frequently, and the trip takes about 20-25 minutes (if you're on one of the faster buses, that makes fewer stops). The front desk at the HI Express had printed bus schedules available, but they are also available online, at the NJTransit website.