Have been a huge fan of Lupa for more than 8 years. Unfortunately, the last 2 times I went this past year it was quite mediocre bordering on bad (overcooked pasta, sloppy service etc). I asked a friend who knows the partners and apparently the Dentons sold it. So...my advice is to skip it. Locanda Verde is quite good, also Gemma at the Bowery Hotel. Emilio Ballato's is a hidden gem, but pricey.

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Lupa
170 Thompson Street, New York, NY 10012

Emilio's Ballato
55 E Houston St, New York, NY 10012

Locanda Verde
377 Greenwich St, New York, NY 10013

Gemma at the Bowery Hotel have a back room that they reserve for large groups. I've been and it's quite good.

Convivio is your best bet with a cute little bar that is perfect for a solo diner. An easy 10 minute stroll east. Alto is also up the block and very good too. Marea is tough to get in to.
As for Lupa, I suspect that the commenters recommending it haven't been in a while. It USED to be great, but the Denton partners sold and it's pretty mediocre over the last year or so. Enjoy wherever you end up!

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Lupa
170 Thompson Street, New York, NY 10012

Convivio
45 Tudor City Place, New York, NY 10017

Marea
240 Central Park South, New York, NY 10019