Good points and info.I agree, at the very least, they should have her leaving the airport. In addition to taxis perhaps ubers (NYC taxis drivers may have the political pull to keep them out of the airport), city buses to key subway stations are very common.
If I remember right, the bus is free- facilitates people leaving the airport. This could make it an attractive way out for a fugitive with a cash crunch. A common bus ride from La Guardia is the one to the Jackson Heights subway station / hub in Queens.
Once out of La Guardia, did she stay in NYC? Going to any "crunchy" town e- ski towns and other trendy outdoorsy towns with a fitness / biking / alt health vibe would seem too risky in regards to recognition. Most rural areas though, would not have those vibes at all.
If she stayed in NYC, are there any "start over" areas for 35 year olds? Perhaps Times Square's vast restaurant / entertainment zones looking for wait staff- with an eye out for attractive employees of either sex? Maybe the Broadway area as theatre support staff or venue staff?
Likewise, I think some parts of Brooklyn (DUMBO and nearby?) have a lot of transplants who arrived due to a tech boom centered on small start up companies. My neighbor's son went for the boom- and now says NYC is his forever home.
One question: How would KA apply for a job without revealing her true name and identity?