I guess the closest, are the Saddle River and Ho-Ho-Kus brook, but near Paramus, trout will be strictly spring stockies.....
If you drive further north (upstream) the Saddle River becomes a WTS. but access is more limited.
South (downstream), in the Rochell Park area, there's a park, that would be easy on a beginner.... You might find some big carp down there, especially in the spring when they're spawning. There's more parkland north of Route 17, but I'm not familiar with how "beginner friendly" it is.