In order to get to the White Sox people commonly take the Red Line, which follows 94 south towards US Cellular Field. The Red Line is mostly underground and they have spruced up a lot of the stations on the way to 35th street.
This weekend, due to chaos and construction on the El, the Red Line was running on the Brown Line tracks which are overhead in the loop, and then switching to a bus, and then back to the Red Line to complete the trip to the Sox stadium. Needless to say this would have been an epic journey even if the CTA were a well run organization, which it isn't, especially on Sunday, when the trains run intermittently during the best of times.
Luckily, for Sox fans, you can also take the Green Line down to 35th. The Green Line runs on overhead tracks, which should make it slower than the Red Line, but really it seemed faster, probably due to a lot of slow spots on the Red Line. Being on overhead tracks, the Green Line is a lot more scenic and you can see all the construction in the south loop and down towards IIT. On Sunday we took the Green Line and we were some of the very few fans to do so... most went the doomed, herd like faux Red Line route.
For people who haven't taken the Green Line in years, I'd recommend trying it from the loop to Sox park. The area near 35th has been totally spruced up; the aging projects are being torn down and few are left; you can see them demolishing the projects in the upper left of the photo, with all the new condos on the rise nearby. There aren't shops or bars yet, but there is street traffic, and you can sense a new vibrancy in the neighborhood. I don't know if I'd press my luck and hang out there at night, but I can see it happening some day in the future, between the improvements on IIT and the surrounding neighborhood and the closeness to the loop.
One unfortunate part of the Green Line stop at 35th is that the CTA, in an attempt to outsmart the taggers, actually hired some local "artists" to put graffiti on the side of the station. Generally the taggers don't paint over someone elses' work, so it has been like this for years. In lots of neighborhoods this is probably a best case for the CTA, but I sense that the Green Line will be moving up and someday they'll paint over this sad cave-in.
My tip - take the Green Line to the Sox Park if it is light out, and maybe even in early evening if there are a bunch of you. Kids will like to see the city from there, and it is less crowded.
I always wondered why the CTA rail system neglected huge parts of the city but then put 2 rail lines parallel to one another... in this case, it works to our advantage.