Not questioning the answer at all, but I'm curious how the locative form of "siłownia" is "siłowni" and not "siłownie" or "siłowny" which my gut would initially go to
I thought the rules for declension of fem. sg. nouns followed three basic rules
koszykówka -> Nie wiem nic o koszykówce
praca -> Jestem w pracy
poezja -> Nie wiem nic o poezji
Is there another rule I've missed or is siłownia just an irregular declension?
Yes, 'w' is an accepted answer.
There are two possible choices:
1) na + locative to indicate location (ćwiczę na siłowni) and na + accusative to indicate direction (chodzę na siłownię).
2) w + locative to indicate location (ćwiczę w siłowni) and do + genitive to indicate direction (chodzę do siłowni).
I believe that there is no difference in meaning between those two. However, the Polish National Corpus suggests that there was a 23% decrease in usage for option 2) but a 27% increase in usage for option 1) when comparing the pre-2004 period with the post-2004 period.
So I conclude that option 2) gets more probable the older the speaker is. Linguist Prof. Bańko also took a look at the corpus results and seemed surprised that 1) is already several times more common, as he himself would still prefer 2).
However, according to Wikipedia, he was born in 1959, which could explain his preference.