I have a very late (11:30 pm) departure to Delhi in October. Will be flying in the day before and spending the night. So opinions on booking 2 nights and leaving for airport later versus checking out at normal time and spending so many hours in the lounge.

I haven’t been to the Polaris Lounge in years. Reviews seem mixed on flyertalk. Thoughts?

Depending on the hotel you stay at checkout time is usually between 10am and 11am. If you have an 11:30pm flight that means you’ll be spending 12 hours in the Polaris (or other) lounge. Regardless of how nice the lounge may be that’s not something I would look forward to. If it were me, I skip the lounge and book the hotel room for the extra night. Relax at the hotel during the day and use its facilities, have a nice dinner than go to the terminal at the appropriate time to catch your 11:30pm flight. I’d stay at the Marriott which is on airport property and offers free shuttle service to the terminals (only a10 minute ride).

AFAIK the Polaris Lounge closes at 10:30 so you'd still have to kill some time in the terminal. 12 hours in a lounge -- even a Polaris Lounge - would be a gawd awful slog. I'd agree re the Marriott

In our experience, the Polaris Lounge at Newark can get very crowded starting in the afternoon through the evening European departures - better than the terminal for sure, but not all that relaxing.

I had my two flights mixed up. My flight out of Newark leaves at 9:30 pm, but I’m still thinking of doing the two nights rather than all day in the lounge.

I am flying fro BOM back to DEL and spending the night before my international flight home. That is the 11:30 pm departure so will probably do the same thing.

EWR Marriott is OK, we've used it a couple times and found it adequate but not anything special. There's also an EWR Holiday Inn Express that runs a free shuttle from the terminals which is pretty OK. The Crowne Plaza is not as convenient and is in a pretty sparse neighborhood. The other mid-range properties are across the freeway. Wherever you wind up booking, ask about the possibility of a late checkout rather than booking an additional night which you won't really use. If the occupancy rate is low they may comp it (especially if you have any status with the chain) or may allow it with a charge that is less than a night's stay.
For your flight departing at 9:20 you'll want to be at the gate by 8:30 or so as Polaris will be among the first boarded. If you can get a late checkout on the day of departure - say, 1 or 2 PM - you'd have about 5 hours to kill in the lounge. That's about on the edge of tolerable, but the Polaris Club at EWR does have "Quiet Suites" where you can relax, even nap, and you would have plenty of time to do some eating and drinking prior to your 14+ hour flight to Delhi either from the menu or buffet style.