One of my biggest frustrations on crutches was finding taxis in places or times of poor bus service. Even more frustrating was watching people basically cut me in line for the next taxi by either running ahead of me or just standing further up the block than me, snagging the next available taxi. Furthermore, it was most often the case that the taxi would stop for pick-up or drop-off in a lane of moving traffic, the cross walk or (much to my chagrin) a bike lane.
All of this may change in the future if the Taxi & Limousine Commission follows some of the advice of the Design Trust’s "Designing the Taxi," (PDF file) which looks at many revolutionary new ideas that would transform how the taxi system operates. But specifically, this photo of a mini-taxi stand that a person could walk up to, press a button and have a light pop-up for any taxi to see and for them to look for intrigued me with it’s beautiful simplicity. Taxis could also simply take a quick break in one of these to wait for a person to enter the taxi, preventing endless cruising around the city.
A good start in Manhattan would be to situate these every three to four blocks on the main avenues and then also between every avenue on the main crosstown streets. In the outer boroughs, these should be located in areas without good mass transit service and near major shopping destinations. All it would take to have a safer, more convenient, high class taxi pick-up and drop-off system is giving up a few dozen free or metered parking spaces per neighborhood, which may be a nice side benefit in that it would reduce the incentive to drive to that area and take mass transit or walk instead.