I highly recommend riding the Bx4/4A, Bx15, Bx41 and if you want a complete bronx project tour the Bx36 Don't ride the lines at night...just sayin' lol
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Here are the route's I've ridden on:
Bronx:
All sans the Bx16, Bx24, Bx26, Bx28 and Bx29 (Not a big fan of Gun Hill lines I guess lol)
Brooklyn:
B54, B57
Manhattan:
M14A/D, M15SBS, M20, M34SBS, M42, M50, M66, M96, M100, M101, M102, M103, M116
Queens:
Q22, Q33, Q44, Q110, Q113
Staten Island:
None
Express: BxM10