In most cases, indoor spaces are private property, and you always need permission to photograph on private property.

Even quasi-public spaces like shopping malls are private property.

Publicly owned indoor spaces such as City Halls are exceptions, but in the post-9/11 era, going in with a tripod is going to attract attention. So asking for permission is always prudent. And be aware that using a tripod during periods of heavy pedestrian traffic might be a safety issue, so your timing could be an important factor in whether you receive permission.

I once did photography in the very grand train station in Utica, NY - the station master was more than happy to grant permission because he was proud of his beautiful building.