Ask HN: West vs. Midwest?

This is my final year of undergrad.

I have a new-grad software engineering offer with one of the FAANG companies. I can choose between the Bay Area and Seattle. Base comp is a bit over 100k plus RSU's (a reasonably standard offer I think). I might try for more offers out in the Bay Area, but I liked my experience at this company so far.

I have another offer with a startup in Chicago. While I don't have exact details yet, I expect a base comp that's a little under 100k plus equity vesting after some cliff (pretty good for the area, I think). The company is well-funded and has a very interesting and difficult problem to solve with under 50 engineers so far. In general they do work that I don't think anyone else is really doing and everyone there seems to really believe they'll be successful in a few years. I think so too.

My concern is that taking a new-grad offer with a midwestern startup might label me as a midwestern startup engineer (after this startup exits). In other words, companies might not be as willing to hire me unless I'm looking in the midwest. I think tech in Chicago is growing, but if it doesn't and I want to go work a FAANG company elsewhere in my later 20s/30s, I don't want to be caught out of luck.

Are my concerns valid, or am I being unreasonable? Does anyone have any thoughts on how I should approach this?