That said, pin stripes say business so definitively that they should not be worn away from the office, unless it is to an after work event where no-one could reasonably be expected to change clothes. Worn out of place, they speak to a limited wardrobe as in "I had nothing else to wear." That may be more true than not, but a solid worn in the pin stripe's stead makes no such statement.
Pin stripes should in my opinion always be worn with oxfords, the definitive shoe for the city and business. And since they have a noticeable pattern, they ought to be combined with either a solid shirt or a solid necktie lest things get too complex and others think the wearer pays too much attention to his clothes. Wear a white or pink shirt with suits that have a charcoal ground, and white or blue with navy. Stuff a white linen square in the jacket's breast pocket and top things off with a foulard necktie if the shirt is a solid, or a solid grenadine if the shirt is patterned.
Oh, and by the way, the pin stripes themselves ought always to be off-white or light gray with charcoal, and off-white or light blue with navy.