Svidaniye (Свидание) has several meanings:
- most common modern single-word usage is for date as in “romantic date”
- archaic is for “meeting” that remained in this goodbye form.
So “do svidaniya” is literally for “till we meet again” :-)
As a side note, Russian pronunciation is remarkably uniform compared to languages like English. Dialects do exist but in practice the vast majority of speakers will pronounce things very similarly. The phonetics are also so different from English than the typical English speaker will not pronounce any Russian words close to native pronunciation.
AFAICT, that goes for absolutely every other language too. Nothing even comes close to English for inconsistency in pronounciation (and even more so, spelling).
As the preposition is so small, it's considered together with the following word, which in the genitive has its stress on the "а".