Can't seem to remember.
Kind of like how 当日 means "appointed day," I'm pretty sure I've seen a kanji for something like 当所 but I can't find one. I've found 当地 but I don't know if it has the same implication as 当日.
I found the "当所" entry in 大辞林, which says this word means "this place". But I cannot find the "当所" entry in 新明解. The word "当所" is rarely used, so 新明解 may omit this word.
Since "当所" has a same pronunciation as "当初", which means "at first" or "at the beginning", and a use of "当初" is more frequent than a use of "当所", "当所" used in talks may be confusing.
When I want to say something meaning "a place where the specified event will be held", I use a word "現地".
試験当日
meansthe day of the test
.