Since it sounds like a one in and out, which airport shouldn’t be a big deal. If it was more frequent, From Markham, or anywhere in the vicinity, I prefer ORD. Straight shot from Markham on I-294. But MDW certainly has its hardened fans.

I’d chose Homewood, Tinley Park, Orland Park, Frankfort, Mokena for a long term stay. Markham is convenient to I-80/I-57/I-294 exits from these towns, or most others. Traffic tends to be an issue around 17:00 and on Friday afternoons. But nothing like farther north, unless you are going to Indiana. However once Labor Day hits, things calm down considerably. Either way, consider getting an I-pass, or EZ Pass for our numerous tollways.

Non chains that I like for a bite, on the casual side:
Hog Wild (pork and on Fridays, some of the best walleye you can get). Calumet Fisheries. By the lake, and a drive, but a must for fans of the Blues Brothers. Saigon (Orland Park), Joy Yee for Thai (Tinley Park). A little more upscale is Princess Cafe in Beecher for a supper club environment, Mr Benny’s Steak (Mokena). For real upscale, I tend to hit Oak Brook ( near western suburbs). This doesn’t scratch the many local great ethnic eateries.

Two chains you might consider are 1) Chicagoland’s Portillo’s. They are know for their Chicago dogs, as well as beef sandwiches. They are set to go public in the next few months. 2) Pizza in the area includes Chicago’s own Aurelio’s Homewood location, a real treat for thin crust fans.

About 15 miles west are various locations of the I&M canal, including the bridge that takes the canal over the Desplaines River. Nice walking trails. Further afield are Kankakee and Starve Rock State Parks. You can even take a day tour from the beginning of US Rte 66 through a number of scenic spots.

As far as the city goes, Markham and surrounds are well covered by Metra’s Electric line. Fast and frequent service, including to Museum of Science/Industry and the Museum Campus( Natural history, Shedd Aquarium and Adler Planetarium.) Also Soldier Field where the Bears play Football. Another two stops north is the Art Institute.