Thanks, Matthew.
To clarify, I am looking for what you can claim as Off-Broadway on your resume. To me, the contract is what counts. If I did a NYMF show or a Fringe show at a theatre which commonly houses Off-Broadway contracts, that doesn't mean my show instantly gets Off-Broadway status.
The impetus for my post is that I've had several job offers lately for Showcase Code productions at Off-Broadway venues where the offer email has said "it's low budget, but it's a solid Off-Broadway credit for your resume."