You can also say e.g. "mennä saunaan" with the illative case, and mean "(in)to". If you used the allative (saunalle), that could translate to "to". The adessive (saunalla) would be more "at", I'd say.
Why not se on??
The it in this sentence is a dummy subject (there is no actual subject being anything) and it's not translated, because Finnish doesn't use those.
Is it only the verb käydä that can - in combination with an inessive - be translated as "(in)to" even though this would suggest the use of an adessiv (or illative) in the finnish sentence or is that common (colloquial) speech?