I'm not trying to drive into NYC, but I am curious about the highways. In particular I'm trying to get to Larchmont, NY.
Does it get better or worse close to midnight or after midnight? About how many hours would such a trip take?
It shouldn't be any worse than usual - it might even be a bit light; Larchmont is a ways north of NYC proper, so I wouldn't expect significant NYE related backups there.
One thing that you should be wary about however, is drunk drivers! There will probably be more of them on the road than usual that night, so be cautious and alert. (Similarly, there will probably be an above average number of police along the highway looking to catch said drunk drivers - and they won't bee averse to writing you a citation for any other infraction which they might observe. Drive safely!)
In this case I'd do exactly what Google Maps advises, even though it may seem a bit odd.
This route leaves I-84 well north of New Haven, CT, which is where I'd expect to see most of the traffic issues on this route at any time of day, let alone New Years' Eve, and bypasses it on Route 15 (Wilbur Cross Pkwy), rejoining I-95 well west of New Haven, and hopefully past the traffic you should expect there.
The second route option Google gives follows Route 15 further; it parallels I-95 almost all the way into NYC. Consider using this alternate route if you hear about bad traffic or accidents on I-95 while you're taking the trip.
The Connecticut DOT has transmitters on 1610 kHz (Route 15) and 1670 kHz (I-95).