Ambient covers? I don't think you'll find anyone claiming to do that, other than Bang on a Can.
All the ambient artists I know who have played live are doing improvisation, even if there's a little bit of direction decided-upon in advance. I'd say that common venues for this sort of thing would include art galleries, coffee shops, cafes, bars, clubs, theaters, churches, and planetariums (planetaria?).
Some people here have done more live performances than I have, and may have more to add.
My own favorite performance ever was at The Gathering series in Philadelphia (I played with Dave Fulton and Jeff Pearce in 2000, right after the release of Imprint and Bleed... in fact it was the release party for both CDs), along with a late-night performance live on the air on Star's End radio. I know many other ambient artists who say the same thing about Philadelphia, The Gatherings, St. Mary's Church, WXPN, Star's End, and Chuck VanZyl. I also met many Hypnos Forum people that night (Brian Bieniowski, Stephen Philips, Jim Brenholts, Jeff Kowal, others I'm probably forgetting... I should look for those pictures on my hard drive)