The phrase "a small auditorium at" is correct and usable in written English.
It can be used when describing the location or size of an auditorium in a specific context, such as an event or venue.
Example: "The conference will be held in a small auditorium at the community center."
Alternatives: "a cozy auditorium in" or "a compact auditorium located at".
Fewer than two dozen people attended the meeting, which was held in a small auditorium at the New Museum.
Having self-funded his album Gossy, he got his break in Vegas in a small auditorium at the Palms casino six months ago, and has since found an enthusiastic audience.
The recent show, in a small auditorium at the Ridgewood Public Library, was a warm-up for the chorus's 100th anniversary gala concert, to take place on April 26 at the West Side Presbyterian Church in Ridgewood.
On a recent night in Manhattan, a group of New Yorkers, many of them denizens of the streets below Fourteenth, gathered in a small auditorium at the Whitney Museum for a memorial in honor of the pioneering choreographer Trisha Brown.
On the night of October 5th, a group of Polish students, professors, military officers, and state officials crowded into a small auditorium at Warsaw University to hear Paul Wolfowitz, the Deputy Secretary of Defense, give a talk on the subject of the war in Iraq.
Now, freshly showered, his longish hair going its own way, his biceps stretching the sleeves of his tight-fitting polo shirt, Nadal, at that moment the No. 1 men's tennis player in the world, was seated behind a table in a small auditorium at Wimbledon's press center, weighing what to say.
A small auditorium in Nemours could be converted to a movie theater, Mr. Buccini said.
In a small auditorium, Rockefeller stood next to publisher, O. Roy Chalk, and answered questions.
Inmates were gathered in a small auditorium, waiting — which is what people in prison do, most of the time.
On the other side of the wall was a small auditorium, with a grand piano set up on a stage.
