I used to do this trip weekly and I strongly agree that it is way too rushed of a trip. One day is not nearly enough for Boston and in reality you are looking at just one afternoon since you'll be arriving that day via international flight. On top of that, you will be tired from traveling (unless we're talking a short YYZ-BOS flight or something).

OP also mentions arriving on a Wednesday and driving the next day - well summer traffic on Thursdays (especially leaving Boston), is brutal. You have everyone trying to avoid the even-worse Friday traffic out to the Cape. I am no Amtrak fan, but that is how I would do it for this particular trip with your time constraints. If you are locked into these dates, I would do an extra night in Boston and one less in NYC. South Station is extremely easy, though you will come out in Penn on the other end... You don't even need to bother with the acela, it's marginally shorter (though it is quite a bit nicer than the regional trains). The other added benefit is you will not have to deal with a car in Manhattan and worry about returning it there. One-way rentals can be pricey (though so can Amtrak).

If you do decide to drive, both ways (95 along the coast and 84 down through Hartford) are just highways - not exactly a scenic drive but you do get see some nice towns pass by. The coastal route is far more scenic. I would actually advise against Waze and use Google Maps. Just my opinion, of course, but I find Google Maps has far superior traffic updates and rerouting abilities, should you need that. I frequently find Waze lags behind the real situation. I wouldn't bother with the ferry and doing the Long Island route if this your first time. I think the coastal route down I-95 is your best and most scenic option, as I'll go into below.

I would only drive if you do plan to stop along the way. You have many great recommendations above - I would second Mystic (really charming, some good restaurants, the aquarium is well-known, and the naval history), literally any of the RI coastal towns from Charlestown, Narragansett, Westerly, Newport, Barrington etc. are worth a stop - they are all really nice, have tons of history, and you can get some beach in if you do want to relax a bit. Same goes for the CT side if you want to get a bit further - Essex, Old Saybrook, Lime, etc. They are all charming and the epitome of New England. Any and all of these towns will have B&B's for you to stay in and can easily be searched for on Google Maps/Hotels. The added benefit of stopping for a night along the way to NYC is you should be going against the summer Friday's traffic/mass exodus leaving NYC, so the drive into Manhattan shouldn't be too bad.