Times Square has banned alcohol on NYE for at least the last decade, and the state of Indiana blocks all Sunday alcohol sales, so I expect those two events to be a little more toned down.
You can buy alcohol on Sunday in Indiana as long as it's 12pm or later [0]. And you can bring your own alcohol to the Indy 500 as long as it's not in glass [1].
0: https://www.thehayeslawoffice.com/blog/2020/02/indianas-sund...
1: https://www.indianapolismotorspeedway.com/events/indy500/pla...