This might be your answer:
Fredericksburg apartment For Rent - 2 bedrooms (broken link)
Don't go based on the map that's on that site though... But from the looks of it, it's basically a finished basement apartment. It appears you'd be renting from the people above you, but I'm not 100% sure on that. 2 bedrooms, 1.5 baths, and under $1k a month, which includes high speed internet, washer/dryer/trash pickup/cable TV, and use of the club house.
You said you need a place ASAP, and this ad says that you don't have to pay rent for April if you move in... if it's still available, you might be able to convince them to give you the month of May for free.
The place is in Lee's Parke, which is a new (All homes built within the last couple years) community, less than a mile off the highway, south on Rt. 1 off of Exit 126.
I know you wanted a single family home or a townhome... but this at least is in a very safe area, and is new... not to mention definately within your pricerange.
I'll keep looking a little more tonight for you.

But I doubt I'll be able to find anything better.
*edit*
Oops! I thought you were the same person who PMed me yesterday looking for a place to rent near Fredericksburg for under $1200 per month! I'm sorry for the confusion.
