Anastasia is definitely a choice, but I believe you'll most likely get SRO tickets, since I don't think they have a rush (unless they do now; but I think it's just SRO). The cast are wonderful, and the set is beautiful.
Like others have said, Play That Goes Wrong is absolutely wonderful. I saw the show a few weeks ago, and my rush seat was located in Orchestra row A (the second row) right in the center. I thought it was a fabulous seat, and it was the most hilarious thing I've seen.
A Bronx Tale is also a good choice. I also rushed this show a few weeks ago, and I actually ran by the theatre maybe 20 or so minutes before curtain because my prior plans with friends fell through at the very last second. I got a ticket no problem, and there was at least one other person who got a rush ticket behind me! My seat was located in Orchestra row AA (the first row) on the aisle of the center section. It was marked as partial view, but I honestly loved being that close to the stage, especially because a lot happens at the front of the stage. This show doesn't get much love on these boards, but I have to say that it was a great experience. Sure, it doesn't do anything revolutionary, but it was a well-done musical with a good score that captures the mood and soul of the period, a great cast, and wonderful choreography. I do have to admit that I believe my being so close to the stage made the experience all that more exhilarating and enjoyable, but I am sure that I still would have enjoyed the show from any seat.
This is another play suggestion, but I also really enjoyed Indecent. Its run is ending in a few weeks, so I've been recommending it to as many people as possible. It is an incredibly artfully done piece that tells a beautiful, important, and relevant story. I rushed the show and didn't have a problem getting a ticket; from my understanding, rush tickets for this show are usually in the first row or two of the orchestra, and then in the boxes. I personally got a box seat, which was a partially obstructed view, but it wasn't bad at all.
Best of luck on your interview, and I hope you enjoy whichever show you decide on seeing!