If you're going to at NAS Lakehurst, the most convenient area to look for rentals is going to be Toms River. You should be able to find something decent in a 2BR in that area for $1,200. Just looking briefly, this place came up that has rents starting at $1,050 for a 1BR, but it looks like a pretty nice community...
The Fairways at Bey Lea (Toms River,NJ)
They're advertising 2BR/2BA with a garage for $1,600, so I have to think a simpler 2BR without a garage should be within your range. This search on apartments.com turned up 84 options all in that area with prices ranging from $800 - $1,800+
Apartments for Rent | Houses, Condos and Townhomes Rental Listings - Apartments.com=
Toms River is a decent and safe area, but I imagine some of the older, cheaper apartments can get sketchy. However, that search shows that you should be able to get into one of the nicer communities based on your budget.