I used to live in both, but havne't been going back very much since. so I hope somebody can give you some more up to date stuff. some old school stuff -
there is a place called humous Pinati - corner houmous. it is a hole in the wall houmous place, maybe 50 years old, very good it's on king george street
on agrippas street there is a place called stekiyat hazot (midnight steakhouse) its also an old school grill resteraunt. also probably 50 years old. very good example of israeli grilled meat. get the kabab
go to the market in Jerusalem, mahane yehuda (its close to both of the above) its a cool experience. espectially friday morning
in tel aviv
go to shinkin street and/or the florentine neighborhoods, very cool areas to walk around. if you go to shinkin street, have coffee at tamar cafe.
on ben yehuda, there is a great gelato place called "sicillian gelato"
off of the south corner of dizzengoff and king george in tel aviv is a great swarma place. its huge, I don't remember the name, but you'll see it.