New Yorkers, like many urban travelers, tend to want it all when they take a vacation: a bracing infusion of another city’s culture as well as some rare peace and quiet. The challenge is finding both in one fell swoop (and without an additional schlep through the airport). The itineraries in this installment of our annual “Spring Travel” package are all about striking that elusive balance: pairing bustling cities with tranquil nearby country­sides (and beaches and desert). A shopping tour of Seoul gives way to temple-dining among the bamboo groves of Jinkwansa, under an hour from the city; art-booming Mexico City is coupled with the hour-away Shangri-la of Cuernavaca; and the bright lights of Taipei meet the hot springs of Wulai, just a short bus ride from the city center.