Welcome to Ft. Myers! I know how tough moving can be so I wish you the best of luck in finding someplace to call home! I used to live at Park Crest with my husband - we moved into a house in June 2008. We had lived there for 3 years. I know there have been a lot of changes there recently, new management and such which is probably a good thing. Park Crest isn't bad, very convenient location... but there have been problems there. We lived in building 17, which is right behind the Publix shopping center. There is a sports bar in that shopping center with a porch on the backside and they do have live music there on the weekends. It can get kind of annoying! On a more serious note, Park Crest was great when we first moved in - well maintained, relatively quiet, nice neighbors. Since then, there have been a lot of young people, especially college kids that have moved in, along with their parties. The property manager that was there while we where was also fired for stealing cash that was paid for some of the furnished apartments that they rent on a nightly basis (like corporate apartments - nice for out of town guests). The big issues we ran into were that the outdoor areas were not being maintained (the hot tub and car wash didn't work for 6 months), 2 garages/storage areas in our building (1 was ours) was "cleaned out" by the grounds staff - basically all our stuff was stolen and the management claimed that none of their employees did it even though the sheriff came out and said that there was no sign of forced entry. A lot of things went downhill, but that could have been a consequence of the manager at that point, and she is no longer there.
It's not a bad place, especially on a budget, but I would definitely do my homework and be cautious. There are an awful lot of empty homes for rent in the area too if you don't necessarily want an apartment, you just have to do some digging!
Hope I didn't scare you off... just wanted to give you some history on the place. Good luck in your search!