Northside has no real boundaries, so we'll say north of Madison. South of Armitage, east of Austin, and west to Calfiornia. As you get further into Humboldt Park and Logan Square (east of Homan/Kimball) these properties will become far more difficult to find, but they do pop up.
Additionally, the East Garfield Park area east of California to Western, staying south of Grand, will yield some finds as well.
Heading north of Armitage, upwards to around Diversey, once in awhile Belmont, and west of Kimball will also bring up the occasional cheap cheap rehab, primarily in the section south of Fullerton/wrightwood. Don't bother looking further west than Central.
If you had aspirations of getting your under $70k property in Lakeview, or Andersonville, or Jeff Park, or for the most part anything out of the boundaries I just drew up, it's close to impossible.
Keep in mind loans like FHA 203k or HomePath (for Fannie properties) if you find yourself short of rehab cash. Or consider a cash-out traditional re-fi on your new home where instant equity is possible. And many times it is.
Beware of sleeping squatters when you view some of these places. You may want to bring some cookies to appease them. I find walnut raisin goes best.
If you are looking for a house to move into a couple days after closing and don't want to worry about getting shot, then No.
There are plenty of REO's around to buy for dirt cheap. Condo's for less than $10K. Houses for $30-$40K. The condos usually have major legal issues. The houses typically are not habitable and need major rehab.
I suggest you figure out how big of a project you are willing to tackle and use that as a starting point when looking.
It really depends on what you mean by "around North Side" as that's a pretty broad area. I just checked the MLS and drew a big search area from downtown up to Touhy, West to O'Hare and kept close to the expressway going back South and the least expensive house was $75,000. If you want to go further West or South then you will absolutely be able to find something. May I ask why you are looking to pay cash and not get financing?
3101 N. Greenview Avenue, Chicago, IL 60657