"Last night" is more specific but I don't think anyone would object to calling "tonight" part of "today."
(At night) What did you do today?
(At night) What day is it today?
However, you certainly wouldn't say "today night" instead of "tonight."
I checked my local dictionary for a definition of "yesterday":
the day before today.
My guess is that "day" here implies a 24 hour period. That period includes a night and saying "yesterday night" provides an unambiguous reference to a specific time.
All of that being said, "last night" sounds better and takes less time to type and write. The only reason I can see for saying it is to bug your friends which, in my opinion, isn't good enough.