I normally have no problems with "what else  to serve" with American, Japanese, Mexican, Italian, German, Korean, and Chinese food, but struggle at times with other cuisines when I am having people over.

i will be serving early dinner to my niece and her Greek fiance from Crete in few weeks.  I plan to make make two recipes I've made recently that we loved.  Both are from Milk Street.  

Shrimp, orzo, and zucchini with ouzo and mint

Grilled chicken salmoriglio - although this one is Italian, I thought the addition of lots of lemon seemed very Greek, delicious and easy to make

Besides the ubiquitous Greek salad, what other dishes will go well with these two?  

Thanks for the suggestion of rice but perhaps with orzo I am serving which is very similar to risotto, I will use your suggestion when I am serving without substantial carb dish and grilled meat or seafood. 

I am really new to Greek cooking with the exception of moussaka, tzatziki, greek eggplant spread, souvlaki, stuffed grape leaves and Greek salads but I want to venture out to this amazing array of Greek cuisine from various islands. 

Looks like some stewed vegetables are some common side dishes and I thought perhaps Imam Bayildi (grilled half eggplants) and as you also suggested bean salad with perhaps grilled and charred squid or octopus.  

i saw an interesting dessert in Milk Street called  Greek Apple Cake with Honey and Cinnamon (Milopita) which seems doable as I am out of practice with desserts. Served with sweetened yogurt with honey.  My husband reminded me it is actually next Saturday when they are coming. 

An eggplant dish, maybe fried and served with scattered feta?  Or briami, which is the Greek version of ratatouille and can be made with all manner of vegetables.  Onions, garlic, tomatoes, capers and spectacular olive oil are the only constants.   Another possibility is lighly cooked vegetables that are served cooled, with greek style dressing of olive oil, vinegar and a bit of honey or olive oil and lemon juice.

Thanks for suggestion on using eggplants.  I am thinking the same.  

i have only met him once but his love of Greek cooking especially Cretan came across strongly.  He was surrounded with homemade olive oils and wines growing up.  

My Mother-in-law grew up in Greece (Greek father, French mother, terrific cook) ... I loved her briam, a roasted vegetable dish. A Greek bread with really good olive oil and Za'ater for dipping is another favorite. And a bit of iced Greek mountain tea provides a bit of novelty for the non-Greeks.

I think with Zephyrness and mjes suggestions,   I am going with briam instead of eggplant dish.  I think it will go better with the chicken dish from Milk Street. Greek recipes are so fascinating.