Although I've come late into this topic, I would like to make the following observations.
Th earlier 'definitions' of suitable and adequate are more pertinent in fuel planning but do have some relevance in this topic. Land at nearest suitable airfield with, say, a cargo fire warning, is quite different to land at the nearest suitable airfield with, say, an hydraulic system(s) failure. The former requires a high-speed descent and approach to an airfield where the aircraft can stop on the runway and the occupants leave by emergency exits before being consumed by smoke and/or fire. Such an airfield may not be one that subsequently the aircraft can be recovered from. In the latter case, considerations such as extra landing distance, crosswind limits etc. may affect the crews selection. In the American Airlines case, choice of JFK was made before the engine shutdown, as a precautionary diversion. Perhaps if the engine had failed at cruising altitude, then the crew may have chosen a nearer altitude. The point is that nearest suitable alternate, does not mean necessarily spiralling down to a landing strip within a few miles - it depends entirely on the nature of the problem and the availability of alternates at the time. In my opinion, the crew seem to have arrived at the decision to divert with only one priority - the safety of the aircraft, its passengers and crew. A job well done!