Looks like there might have been a bit of confusion - I'm currently a first year at Stern, but haven't updated my profile on here since I was initially researching programs. Now that that's out of the way, I'll go on and expound a bit on my opinion - that Stern is the better choice in this scenario.
For my classmates that opted out of an M7 to attend Stern, the answer to "how much" seems to be around half tuition. Anecdotally, a good friend opted out of a 60% scholarship at Booth for a full ride at Stern. This number will vary for each individual, but in my case 55% was enough to make me lose interest in converting an M7 waitlist.
I hate to bring this analogy up, but the "bigger fish in a smaller pond" holds some weight in the recruitment process - but in a different sense than typically mentioned. From what I've noticed, it's purely the size of the fish that matters, given that the "pond" contains the same amount of water. Every firms on the street comes to recruit at Stern, aside from Wells and Deutche Bank. The top firms are looking for that fish - regardless of which school they're coming from, as long as the program is good enough. There are a few boutiques that recruit exclusively from Stern, but I'd imagine Booth has it's fair share as well.
Yes, living in the city is a double-edged sword in the recruitment process. The expectation is that you'll be networking quite a bit more often with firms over the fall and will become well acquainted with the subway system. From the perspective of time commitment, you'll be better off making calls from Chicago - but if you hold your capacity to network in high regard, you'll find that you'll prosper more professionally from being in the city, and can "schmooze" your way into interviews; I think people underestimate how much having one or two people vouch for your candidacy helps in the IB interview process, a benefit that you will seldom develop from a more disconnected recruiting process.