120k is plenty to live really comfortably in Chicago.
Great neighborhoods>Lincoln Park>Lakeview East>Lincoln Square>Ravenswood>Andersonville>Edgewater
Andersonville/Edgewater less urban than the others but all your amenities are still walking distance. I prefer these neighborhoods for being quieter but still lively.
Andersonville has gotten real expensive though. Condos are comparable to River North which is just insane to me. Which is why I recommend:
Edgewater. Close to the red line, close to the lake, all the amenities you need in a city, easy access to other neighborhoods (red line). Diverse in a good way, not in a scary way. I think the restaurants in Edgewater are better than the ones in "trendy" Andersonville.
One thing that kinda sucks about Lincoln Park and Lakeview is that you're either close to the lake, or close to the train. You can't have both. The express buses along LSD are nice for commuting but not for everyday getting around. Hence, why I like Edgewater so much.
You can absolutely get by without a car if you stick to the red line and brown line corridors. I moved here with a car and I'm selling it soon. I never use it. It's more hassle than it's worth.
If you're so sensitive that you can't handle the occasional crazy and if black people "scare you" then you probably have no business in a big city anyway. I've seen some shit on the red line, but never to the point I felt my personal safety was threatened. And if it is, just change cars. Super easy fix.
It's not perfect, but for the things I prioritize (walkability, access to transit, awesome people, plenty of things to do), my quality of life is much higher here than other cities I've lived (Seattle, Vancouver, Austin). I highly recommend Chicago