Barrels under a $100 that are not shot out will be impossible to find.
However, there is good news. If you can save up an additional $69 you can get a really great barrel. Daniel Defense is going to all Cold Hammer Forge barrels. In the meantime they are selling their regular barrel for discounted prices.
Their regular barrels are great. They are 16 inch chrome lined 4150 steel with 1/7 twist. They have 5.56 chambers and M-4 profile. I bought one after Christmas and it is a great barrel. It is accurate and reliable.
There are several places to get one. PK Arms, Bravo Company and even DD. There are some other companies that sell them like Midway but I don't know if they have them is stock.
Now for $169 you get a striped barrel so you will have to buy a few extra parts to mount it.
Here is a picture of the one that just built.

By the way, this was a cheap AR to put together. The barrel was on sale and I got the Spike's lower for $60 on sale. I bought the KAC rail for $105 off the EE on ARFCOM. I even got the mini ACOG for a great price ($450). Not including the scope I just barely have $600 into the rifle with the rail.