You've probably already made up your mind at this point, but maybe not. DaLuciano's is a dream experience for anyone with Celiac Disease. We have tons of options and can get a complete meal and by complete meal I can get garlic bread to go with my entree or salad and can have a real dessert, like cannoli, not just a scoop of boring ice cream. Having said that, there are a couple of downsides to DaLuciano's. The ambiance is or rather was a little lacking as it's very brightly lit and it is indeed in a storefront, but then again if your aim is the GF food then the ambiance is second to the food experience. I was last there about a year ago and the expansion wasn't completed so I'm not sure how it is now, but it's a generally bustling busy place in tight quarters that could be loud. Lastly and probably most importantly, do NOT even attempt to go there without a reservation. They seat anyone with a reservation before those without, regardless of how long one has been waiting.
I've been to Adobo Grill a couple of times and have never been wowed by it. While they do have a pretty good GF menu, they don't offer GF corn or tortilla chips to go along with their signature guacamole and that baffles me. I wish they would just go buy a bag of chips and keep them for people with CD. Sadly, the chip issue is a reason I don't go there.
Of the options you presented, I would choose DaLuciano's despite the ambiance issues.
Fattoush is another restaurant that has a great gluten-free menu and even offers a GF pita bread. However, their Check Please episode recently aired and it might be a little crowded.
Fattoush
2652 N. Halsted
Chicago
773-327-2652
http://www.fattoushrestaurant.com/