+1 to Toyota Corolla, very reliable, efficient, and reasonably priced. KBB.com can give you a good price point, but most people won't sell their car for quite as low as the KBB price. a 2006 Corolla with around 100k miles could be had for 6.5k, MPG 26 city 35 highway
Mazda 3's didn't become very efficient until 2012, and to get something that new you are looking at about a minimum of $12,000.
Some other options,
2010 Nissan Versa, 50k miles 8K MPG 26 city 31 highway
2011 Kia Forte Hatchback, 40k miles 10k MPG 25 city 34 Highway
2010 Pontiac Vibe/Toyota Matrix 50k miles 10k MPG 26 city 32 highway
2006 Scion XA 80k miles 6.5k MPG 27 city 34 highway
2006 Chevy Aveo(made in Korea) 80k miles 2.5K MPG 22 city 32 highway
2010 Toyota Yaris 40k miles 9k MPG 29 city 36 highway
2010 Honda fit 50k miles 10k MPG 27 city 33 highway
These are the cars i've been looking at myself.
I recommend searching craigslist for the best deal on one of the cars listed above that you like, try to buy from a private seller as it's cheaper. Make sure to have them bring the car to a mechanic to do an inspection before you buy it. A lot of mechanics will do inspections for around $50-$200, just call and ask, preferrably get a mechanic from the correct dealership, example if you are looking at a corolla, have a mechanic at a toyota dealership inspect it.
