Alot of bike stores in the Columbus area where I live have single speeds/fixed gears for relatively cheap. They aren't amazing but pretty nice.
BUT if you were feeling adventures, you could pick up a cheap road bike from a used bike store and buy a single speed conversion kit. That is usually very inexpensive. The problem with older bikes is that sometimes they need a little more fixing up then you expect.
You could replace the fork, just make sure you get the correct size, and also you maybe need to buy a fork that is threaded. It is possible.