Hello, intrepid traveler! If you've made Labor Day weekend plans to catch this year's Texas Longhorns-Notre Dame Fighting Irish game of footballs, you're probably flying into Chicago and staying thereabouts for most of your non-gameday experience. Having spent the past two years living in Chicagoland, I'm here at your disposal to provide some friendly unsolicited advice.
Public transportation from O'Hare (via the blue line - $5) and Midway (via the orange line - $2.25) is easy and economically efficient. Travel time to downtown is typically an hour from O'Hare and 30 minutes from Midway; cab fare is approximately $50 and $30, respectively. Note that it's not uncommon for travel time from O'Hare to reach 60+ minutes during rush hours. Non-surge Uber will be cheaper back to either airport.
If you have not yet secured lodging during the very popular Chicago season known as "not winter", may Rahm have mercy on your soul. Hotels that you would actually want to stay at are concentrated either in downtown ("The Loop") or near Magnificent Mile on North Michigan Ave ("River North"). For shared economy advocates, try to find housing close to an "L" (subway) stop. Neighborhoods like South Loop (red/green/orange), West Loop (green/pink), Wicker Park (blue), and Lincoln Park (red) are all good options.
Public transportation in Chicago functions better than almost any other US metropolitan city. Traveling anywhere outside downtown via the L or bus can get time-consuming if your destination is not located near an L stop, but cabs and Ubers are plentiful. Renting a car is wholly unnecessary unless you plan on driving to South Bend.
* - reservations recommended
^ - no reservations available
If I have but one piece of advice when it comes to Chicago food, it is this: get thee to Au Cheval^. There you will order the single cheeseburger (which is two patties) with a fried egg. It is the best burger alive. You may so choose to order a double (which is three patties and slight overkill), add bacon (thick-cut, medium overkill), and/or foie gras (gluttonous, complete overkill). The wait, unless you queue before it opens, will be long. It is worth it. Put your name down, go somewhere else, wait for a call. Consider it part of your West Loop night out. I recommend The Publican* (or its charcuterie and sandwiches sister, Publican Quality Meats^) for an extensively good beer list and tasty salty pig parts. If you're feeling fancy pantsier, try to snag reservations to Girl & The Goat*, arguably Chicago's most trendy new-American restaurant, followed by the most expensive cocktails you can possibly drink at The Aviary*. For Sunday brunch, Au Cheval, Publican, or G&TG's sister restaurant, Little Goat*, are all solid options.
If you prefer staying closer to Magnificent Mile, my personal favorite un deux trois progressive evening starts with dinner at a Rick Bayless restaurant--XOCO^ for counter casual, Frontera* for fancier sit-down, Topolobampo* for the Michelin-star experience--followed by banana dolphin daquiris or your tiki drink of choice at Three Dots and a Dash*, culminating with a stop at Firecakes^ for some midnight donuts. If you're more a scotch-cigar-steak-type, try a double dip with steak frites at Bavette's Bar & Boeuf* followed by a martini and chocolate creme cake at neighboring Gilt Bar*. Both are Brendan Sodikoff establishments, purveyor of the aforementioned Au Cheval. At night, check out the bar scene on Hubbard Street, akin to Austin's Warehouse District. Also worth mentioning as food options are New York imports Eataly*^, Shake Shack^, and Halal Guys^, all of which have outposts in Chicago's River North area. The Loop's dining options aren't as robust, but the newly opened Chicago Athletic Association Hotel*^ has an diverse mix of restaurants (including a Shake Shack) to go along with historical restoration and a great rooftop view.
If you're more the Rainey Street type, check out Wicker Park and Logan Square, the hipster and hipsterer parts of Chicago. Big Star^ and its tacos and patio (plus its $3 bourbon shots) give Torchy's a run for their money. Those in need of additional refreshments can check out the cocktails at Violet Hour*, part of the vaunted Paul Kahan empire (whose restaurants include Publican and Big Star). A more West Sixth nightlife type-feel can be found on Division Street. Nate Silver's favorite burrito joint, La Pasadita^, also resides around these parts (give me SF's El Farolito or La Taqueria any day, but to each his own). Head further west and you're in Logan Square. Here, start with a beer or three at Revolution Brewing^ (my favorite: Cross of Gold), followed by arguably the cheapest, most casual Michelin-starred restaurant in the country, Longman & Eagle^. Its whiskey list is fantastic, as is the wild boar sloppy joe. Smoque^, located just beyond these borders in Irving Park, is generally considered the best BBQ in Chicago. Skip the brisket (looks the part but falls flat on taste) and the Mikeska's-sourced sausage and opt for St. Louis ribs and SEC-influenced pulled pork instead.
The post-college crowd tends to migrate to nightlife in Wrigleyville, but unless you're headed to a daytime Cubs game, I'd avoid. Aside from Wrigley, the North Side tends to be more laid back and family-oriented, inclusive of neighborhoods like Lincoln Park, Lakeview, and Uptown. The best food option up there is the casual Crisp^ and its Korean-flavored chicken wings. I also like Demera*, an Ethopian joint in Uptown that happens to be located nearby The Green Mill*, a legendary jazz venue. And if you somehow managed to secure reservations at Alinea*, I feel completely jealous of your stomach and completely sorry for your wallet.
Finally, a quick note on Chicago's big three: deep-dish pizza, hot dogs, and Italian beef. I side with Jon Stewart on the pizza (it's lasagna with bread!), but if you must, try Pequod's^. More likely, you'll end up at one of the big three chains: Lou Malnati's^, Giordano's^, or Gino's East^. I like them in that order. The very famous and very delicious Hot Doug's used to be everyone's recommendation for hot dogs, but Doug voluntarily closed up shop last summer. The river north location of Portillo's^ is a solid substitute, convienient to get to and easy enough to double-dip with an order of both a Chicago dog and Italian beef. The original Al's Beef^ on Taylor also works for the latter. Personally, I'd instead recommend getting lunch in the French Market (think Ferry Building or Chelsea Market) in West Loop. There, you'd head straight to Fumare Meats^ for its amazing Montreal smoked pastrami on rye.
The two most touristy photo opportunities are The Bean in Millennium Park and the Chicago Theater sign on State Street. The Bean counts as a solid central location from a lot of other stuff. It's walking distance to the Lakeshore, Maggie Daley Park (fun for kids and adults alike), Grant Park, shopping on Magnificent Mile and State Street, Buckingham Fountain (another good photo opp), the Michigan Ave bridge (likewise), and The Art Institute. For workout fiends, Lakeshore Trail runs 18 miles along Chicago, and is great for running, biking, or ambling.
My favorite museum is The Art Institute, home to famous paintings like Hopper's Nighthawks, Wood's American Gothic, and (a favorite of both me and Cameron Frye) Seurat's Sunday Afternoon. If you're willing to make a trek south to Hyde Park, The Museum of Science & Industry is also a great way for a day to fly by. The Field Museum and Shedd Aquarium are easier to get to but less fun overall.
If you stick around the Magnificent Mile, avoid Navy Pier and go on an Architectural River Cruise instead. Thank me later. If you want to venture north, Lincoln Park looks pretty similar to its southern counterpart, Grant Park, but contains a free zoo and conservatory. If the weather is good, Oak Street Beach and North Avenue Beach have gorgeous views (...of Chicago's skyline and Lake Michigan).
Want to head the other type of north? The skydeck at Sears Tower really is cool, but don't discount a drink at The Signature Room at 95th atop the Hancock Tower. The beverage you'll buy basically replaces the price of admission, the lines are much shorter, and the cityscape view is better.
That's all, folks. Happy to answer questions in the comments.