The used car that I am recommending these days are 2006 Ford Fusions (Mercury Milan) 4 cyls with manual transmissions.
A huge influx of former rental cars is really driving down their prices fast. If you choose a manual trans it will assure that the car was not in rental service but it is still affected by the price reduction.
If you search sites like autotrader you will find that you can get a 4 cyl (2.3L same as Mazda 3) with less than 40k miles for just under $10k. You can not even buy a Mazda 3 for this price. The cars seem to be well put together and even the most basic version will have more equipment and comfort of an Aveo. You will also get the same mpg as the Aveo in a much more respectable looking package.
Some Ford Dealers will even sell them as Certified if warranty is important.
Sample listing:
http://www.autotrader.com/fyc/vdp.jsp?ct=u&car_id=258442106&dealer_id=5647...
If the buyer has to have new, search Ford lots for current Fusions. They are in model switch over right now to an updated exterior and my be dealing on old versions.