One other comment: you might need to reevaluate not having a car. I'm a huge no-car advocate, love public transit, and I think you can live wonderfully in Hoboken or JC without one. But commuting to Madison on public transit is... harder. Driving (reverse commute) to Madison is reliably ~40 min during rush hours unless there's some big accident (happens about once a month). Your commute on the train is likely better from Hoboken than JC as there's a NJT terminal there, but oddly might be easier from NY Penn Station. Downtown JC might be more like 90 min and something truly insane like PATH to Hoboken transfer to NJT to transfer at Secaucus to Madison.

Newark Broad Street might actually get you the commute you want on the train (frequent service, 30 min to Madison) but I have no idea about the neighborhood.