What will a 2-bedroom rental in Near North Side, Chicago cost me per month (per person)?

You might find a few places in the $2400 range, but with everything else you'll pay, especially parking, it's going to run you at least another $400-$500 a month I'd think. And that's for a small 2 bedroom. That's a tough area to find reasonable rent. Most 2 bedrooms will be closer to $3000-$3500 just for rent. I wouldn't expect to be able to live there for less than $1500 each.