Bill ... MOST IMPORTANTLY, as this is their first venture into having music, BE CAREFUL OF YOUR VOLUME !!! ... They are not used to having live music, so anything could seem loud at first ... Better to have them come to you and tell you to raise the volume, then asking you to turn it down ...
I played for a while in an Italian restaurant that had 2 VERY small rooms... I even suggested that it might be too small for music, but the owner had heard me at another place, and wanted me to work there... The complaints about volume came from the wait staff who said it was difficult to hear the customers orders... Now I was keeping the volume really low, but they were not used to having ANY music, so it bothered them ...
Having played very similar venues, I can concur with the suggestion for instrumentals early and starting with some 'light' vocals later...
For instrumentals, bossa rhythms (using bass, drums, and guitar background)always seem to work well with all kinds of songs, such as the Beatles "Michelle", "Yesterday", etc.
As it is an upscale Italian restaurant, I would also suggest you do a search for 'Italian' midi files, and songs by Jerry Vale, Vic Damone, Jimmy Rosselli, etc., especially with LIGHT Latin rhythms, even if only to help you expand your Italian song list.... and while I play a 'technics', I would expect the Tyros has a good accordion sound you can utilize also ...
I am sure you will do well, and keep us posted...
t.