Free-parking privileges at New York-New York and Park MGM and any MGM Resorts garage for qualified MLife tier members are not revoked or changed in any way on game days. So anywhere you can park for free at normal times is good when the VGK are playing at T-Mobile. That's the answer to the free question.
As for the best place to park, that's a little more involved.
The garage at NY-NY is, as you say, the optimal place to park when attending an event at T-Mobile. It's practically connected to the arena; if you qualify for VIP parking, you use a separate entrance that allows you to enter T-Mobile without ever leaving the garage. And Aria South and Park MGM garages also get you close to T-Mobile and are free for qualified Mlife members.
But as you can imagine, they get pretty jammed up, what with 18,000 fans coming to see Knights play. In our experience, you have to come early and stay late to avoid the mad rush around the game. That also holds true for valet parking at the three nearby garages (which you also get for free).
You could also park at MGM Grand or Excalibur, but from those garages to the arena is a pretty long walk -- each way. Valet parking at MGM Grand saves you the long walk through the parking garage, but given that MGM's porte-cochère is at the east side of the casino, your walk through the casino, up the escalator, across the pedestrian bridge over the Strip, then through NY-NY or the Park is a hike.
Valet parking at Excalibur does get you a little closer.
You have a few other choices, mainly centered around the two trams.
You could park at Bellagio, for example, and take the tram to the Aria/Park MGM stop, but you probably wouldn't avoid the crush. These days, that tram runs on only one track. So instead of a tram every two-three minutes, a round-trip takes more than five. You might have to wait for a while behind hundreds of other people.
The other alternative is to park at Mandalay Bay or Luxor and take the tram north. The Excalibur terminus puts you right at the bridge over Tropicana Avenue and delivers you right to Arena Drive, from where it's a fairly short walk to T-Mobile. You don't want to park at Luxor, because the tram doesn't stop there southbound, so you'd have to go all the way to Mandalay Bay and double back to Luxor on the way out.
All in all, it seems to us that the best play is simply to plan on getting to the garage at New York-New York early and staying there, or at Park MGM, late to avoid the crowds. If you want to arrive closer to game time, you can try the valet at Excalibur or park at Mandalay Bay and hop the tram.
