Bikesdirect.com is your friend. A new Winsdsor for $300 delivered, or a Mercier (which has a nicer fork) for $350 is hard to beat.
You can probably find a used fixie on craigs for about that much, but you will be hard pressed to convert anything to even a medium quality fixie for $350.
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Il faut de l'audace, encore de l'audace, toujours de l'audace
1980 3Rensho-- 1975 Raleigh Sprite 3spd
1990s Raleigh M20 MTB--2007 Windsor Hour (track)
1988 Ducati 750 F1