This is almost always, save for a few choice cities, a consequence of over-spending. You can look this up on Zillow right now. West Coast and low-housing stock towns on the East coast are going to be difficult even at that income but most of America (including LA, Chicago, and NYC) can live on 100k a year fine.

Your take home pay in LA would be: $6k. 30% of that is $1800. This is what Zillow has in that range

846 total apartments.

I live in Chicago and can tell you 100k is A LOT. It'll go much farther than NYC or LA here. It's roughly the same take home (like $50 more in Chicago). $1800 a month is a ludicrous amount for a Chicago apartment. It's near the low-end of luxury apartment level. Zillow has 3400 apartments listed.

Now, NYC has its own income tax. So, your take home is lowered to $5730. That gives us about $1.7k. Definitely tougher. Zillow has ~150 listings, and about 350 is you expand into the NJ side (right next to Manhattan). You can't live in Manhattan for that. Either way, still doable.