Adding a couple more thoughts.
Forgot about Butcher and the Boar. I've never been, but you might want to inquire of them.
I'm with a group that is at the Hyatt next week, and the group has planned a happy hour (not full dinner) in the Taste Wine Bar section of The News Room. I don't recommend The News Room. But Taste used to have its own menu and chefs. Don't know if that is still the case or not.
BB has it right....nothing in the "latest" category within walking easy walking from the Hyatt that I can think of. He had added most of my ideas, but I'll add a couple of more.
Instead of the Local, Brits is closer and has better food IMO. Still pub fare, but they can accommodate 20 with a bit of planning and in a private area. 11th and Nicollet, so 2 blocks from the Hyatt.
Another thought is Solera, which is maybe 9th and Hennepin. If the night is nice, no worries about a 6 block walk. If the wind is blowing in the winter, then this might be a bit far. Tapas and such, but a lot of private areas and they can set you up.
I don't know if the Butcher and Boar can accommodate private parties (certainly not on weekends), but that is probably the "latest" place on that end of downtown.
There isn't a "latest" restaurant near the Hyatt, but there are several good restaurants near the Hyatt that were the "latest" once upon a time.
Vincent has a semi-private room (their mezzanine( that will comfortably fit 20. If you are all staying at the Hyatt, it's a short walk.
One block further is Masa. No separate seating area, but they will accommodate your group with enough notice.
Not too terribly far away (but a cab ride regardless) would be Gather at the Walker Art Center. They are only open for dinner Thursday - Saturday, but are avialble to cater a group onsite on a Tuesday or Wednesday. They are certainly in the "latest" category.
Porter and Frye in the Hotel Ivy three blocks away would also have space to accommodate your group.
The Local three blocks away has private seating upstairs, and is okay if your group would like Irish pub fare.