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I can recommend two places to eat. A food truck and a Portuguese restaurant.

The truck parks daily in front of York College on Guy Brewer Blvd and has a very short menu. Lamb and chicken served gyro style or as a platter. Both are excellent choices and the food is quite reasonable at about $6 a plate.

O Lavrador is a Portuguese restaurant on 101st Ave and specializes in seafood, but their steaks are excellent as well. A couple of meals with appetizer and dessert (get the flan!) will be around $100 with drinks.

I have not eaten there, but I hear good things about a Plate of Soul. http://www.plateofsoul.com/

https://www.google.com/maps/preview#!q=jamaica+ny&...

The thin red lines on the map in the above link are the official boundaries but colloquially the are is larger. For example, you need to extend the are north as far as the Grand Central Parkway and include the area known as Jamaica Estates. In fact, above that ST john's University is included as being in Jamaica. If you include the area underneath the zone on the map as far as the Belt Parkway you would not be too far off the mark.

Activities and attractions I can't help you with.

Here is more information, than you can shake a stick out. http://en.wikipedia.org/wiki/Jamaica,_Queens