Providence lunch,dinner. Friday & Saturday??
Very little Greek or Lebanese in the area you don't already know about, from the sound of things. Haven't been to Opa recently, but it has a solid reputation. Not personally a fan of Andreas on Thayer.
Lots of Italian chat is searchable here on the board, but my favorite is Siena on Atwells.
Not a local but I have visited Providence a lot. Unfortunately I can't recommend anything in the cuisines you prefer- the only Italian-ish place I have been to more than once is Al Forno and I've had erratic meals there (really good to "not so great for the price"), so I can't wholeheartedly endorse it. Never been to Opa.
But since you mention "any cuisine" here are a few I like. I don't know your pricepoint, but I really love Gracie's and Chez Pascal. I also like Local 121.
194 Washington St. Providence, RI 02903
960 Hope Street Providence, RI 02906
121 Washington Street
Providence, RI 02903
For lunch I love Farmstead's sandwiches and cheese, and Duck and Bunny for lunch nibbles and cupcakes. Sentimental favorites are Spike's for hotdogs and Geoff's for sandwiches.
186 Wayland Avenue, Providence, RI 02906
Duck and Bunny (service can be really slow here
312 Wickenden Street Providence, RI 02903