Because the closest airport to me doesn't have a direct flight
The closest airport to me doesn't have a direct flight to A, so I need to transfer at B
My nearest airport doesn't have direct flight to A,so I gotta transfer in Bはほぼ完璧ですね!ですので直したのは細かいことだけです。My nearest airportは通じますが、The airport nearest to meやthe closest airport to meの方が自然ですね。また、direct flightの前にaをつけますね。transfer in Bじゃなくtransfer at Bと言います。
ご参考になれば幸いです。