I like Virtue Feed and Grain, the upstairs room, for events. Beautiful space, right by the waterfront. Plus good food on site.
Not sure about projector though.

We had a meeting several years ago at the Lyceum.

Not sure if they do anything off season but Nats park rents out conference rooms and the clubhouses for events on non game days

https://www.mlb.com/nationals/ballpark/events/indoor-venues

We have about 10 people gathering for an onsite and we want to rent space for a couple days for meetings. A projector would be good, but not essential. It would be great if it could be unique space since most people are from out of town and we want to make it interesting. Any recommendations would be welcome.