American Airlines has round-trip flights from San Antonio (SAT) to New York, Salt Lake City, Minneapolis, or Detroit (JFK, SLC, MSP, DTW) for $150 with a connection. Flights January to March. Departures on Monday, Tuesday, Wednesday, Thursday, and Saturday. Extended weekends available.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.