Are you only looking to buy brand new or are you open to buying used?
I have bought at least 10 bikes pre-owned on craigslist.
I get great value and if there is something that is not perfect I can change it (I have a local mechanic that has served me well). I estimate I have saved $4,000 to $5,000 by buying pre-owned.
My most recent purchase was a Fuji Feather single speed. It was a 2013 model and I got it for $200. I love this bike. Did I mention: I love this bike.
You can get a lot of bike value in a single speed for under $500. And yes you can always change a seat or change a gear or change the handlebars on a bike you buy for a few hundred dollars and still come in way under your price point. (Many times people buy new and then ONLY AFTER they ride it do they realize they need something changed so the argument that you get what you want when you buy new is simply not accurate in my experience and observation of others).