Personal favorite is the Aloft Secaucus. They’re a boutique hotel and pretty trendy, but there’s an indoor heated pool, game tables in the lobby as well as some arcade games. It’s also a few minutes away from American Dream, if you wanted to go for more activities.
The rooms are spacious but modern, and while the toilet area has a door, the shower area does not (though the glass shower door is blurry). There are connecting rooms and it’s not very expensive, so I guess it depends on your needs. I’ve been there a few times with my toddler and he loves it