What's a good bike for around 300 dollars?

$300 is not going to get you much, unless you go used. That said, it sounds like a "hybrid" might do the trick for you. If you insist on buying new, I would advise you to move up to the $400 range if possible.
 
You need a road bike hybrid. a strait handle bar road bike. Some like this!
http://www.trekbikes.com/us/en/bikes/bike_path/

here is a good one for just over 300.

http://www.schwinnbike.com/usa/eng/Products/Road/Road-Specialty/Details/1377-S10CUT-Cutter

look for year end close outs too. Most shops are trying to get rid of last years models.
 
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