Greek Island's is my family's favorite restaurant so I go there frequently, and it never fails if you are looking for a fun, Greek restaurant with superior food at a great price.
Although the restaurant is huge, it's composed of various rooms that make it feel cozy. The decor is very Mediterranean - bright and friendly and warm. They host a lot of large family parties who are looking to celebrate - so the place can be somewhat noisy. My favorite room is off to the right of the entry way, closest to the bathrooms, where some of the tables are slightly elevated and you look down on the chefs preparing the food.
The place offers a nice variety of traditional Greek food. For appetizers, I recommend the calamari which always comes out crisp and not too greasy, the gyros, spanakopita, taramousalata are all wonderful. For a small group, you can easily make a meal out of 4 - 5 appetizers.
For entrees, the Chicken rigonati with its tangy lemony flavor is a healthy option with plenty of flavor. The moussaka is really tasty lamb dish but not for those who fear rich food. I would also recommend the fish of the day and the grilled octopus. But those are my favorites - rest assured, all the entrees are great.
The baklava is not to be missed - always flaky and rich.
Perhaps the best thing about Greek Islands for out-of-towners is the accessibility from down town (Greek town is west of the loop) and the fact that they offer FREE valet parking. For those who remember this as a questionable neighborhood it has become increasingly upscale in the past few years and shares a similar feel the the tony strip of Randolph which is just north of it.