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For Italian, Coco Pazzo Cafe is close by. And Cafe Iberico is excellent for tapas.
Among Rick Bayless's restaurants, I prefer Frontera Grill or Topolobampo to XOCO. XOCO has conventional Mexican food, whereas the cuisine is much more creative at Frontera/Topo. If you go to Topolobampo, go at lunch (dinner won't meet your "cheap/moderate' criterion) and make a reservation in advance. If you go to Frontera Grill, arrive early to avoid long waits to be seated.
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Frontera Grill
445 N Clark St, Chicago, IL 60654Topolobampo
445 N Clark St., Chicago, IL 60610Cafe Iberico
N Lasalle St Chicago IL, N Lasalle St Chicago, ILCoco Pazzo Cafe
636 N St Clair, Chicago, IL 60611 -
There are lots and lots of great restaurants close to where you're staying. As mentioned, Rick Bayless' places are good- Frontera and Xoco. La Madia, which has thin crust pizzas and Italian and a great wine selection is a great spot. For more unusual offerings- try the Purple Pig, which is right off Michigan Ave and is small plates so you can try a lot of different things. For Asian- I love Sunda.
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XOCO
449 N Clark St, Chicago, IL 60654 -
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Most of the restaurants in the area you're staying in (River North) are pretty touristy or run-of-the-mill (Chili's, Rainforest Cafe, McDonald's). However, there are a couple of more local restaurants you could try...
Quartino's (small plates Italian) is on Ontario and State. always very crowded and a very lively atmosphere
Xoco is Rick Bayless's "fast food" Mexican. Get a torta there. Skip the specialty hot chocolate
Also by Rick Bayless next door is Frontera Grill.
Lou Malnati's and Giordano's also have locations close by if you're interested in Chicago style pizza. (Uno's and Gino's East are also nearby by not nearly as good in my opinon) These will be VERY TOURISTY though.-----
Frontera Grill
445 N Clark St, Chicago, IL 60654Quartino
626 N. State Street, Chicago, IL 60654XOCO
449 N Clark St, Chicago, IL 60654 -
