There is a chinatown bus that will get you from Hartford to NYC for $15, but the times won't work out for you, it's only an afternoon and evening thing.

Not sure what it costs to park in Waterbury, many of the metro north stations offer free parking from noon on Friday to 4 am on Mondays, but you will probably be overlapping that. For some insane reason it's $12.50 off peak each way. Bridgeport or New Haven would have way more trains and more reliable service, but even though the trains go through Bridgeport, they cost more to get there (makes me wonder if a ticket from waterbury would work in Bridgeport or not to save money)

There's a 9:17 that gets you into Grand Central at 11:40, from there you can take the bus to Newark for another $14 (or $23 round trip). The bus is like across the street from the terminal. The bus runs every 15 minutes, takes a bit less then an hour to get to the terminals.