What's the best restaurant in the downtown area for private dining? I'm hosting a dinner meeting and need a private room. TIA

This need to be fancy or no?

How big of a party?

Without knowing details, I'd suggest Moonshine or Bobs

Perry's

Vault at Perrys is always a good time.

+1 for Perrys Downtown. Thats a fancy choice, if you are looking for a different feel:

Oasis Brewing Company's Tap Room (NOT the Oasis Restaurant. Also not Downtown)

La Condesa (Upstairs at Malverde)

Not sure what vibe you're going for but I've sat in the private room at Lin's.

https://www.linasianbar.com/menu/

https://instagr.am/p/Cak4IJ4l_3T

It could probably seat about 8-10 if I recall.

Perry's is a solid choice. I've also used the III Forks room four times, and it's another good option.

Fixe has a couple private rooms.

Malverde above La Condesa, as mentioned above, is a good choice. But the two balconies are largely worthless this time of year (too hot). However, I strongly encourage you to contact La Condesa about the cellar dining room. They used to store foodstuffs there when it was a railroad depot. It's down two steep staircases and some short archways. So if your group is on the older side, gonna be tough. But it is such a great space and only a few hundred Austinites have ever dined down there. There's a small pre-function area where you can do cocktails/wine and passed appetizers, then you slide through this other short tunnel and it opens to a long dining table that comfortably seats about 20. And it's deepest, it's about 20+' below street level. It's really cool and they do a good job customizing a fixed menu for your guests so it all comes out about the same time since the logistics that deep are an issue. Really great experience, can't recommend it enough and it's not crazy expensive.