I have always had luck with used hondas & toyotas (i've had three corollas & an integra) & all of them ran very well. And i sold all of them off while they were still worth something (with 90k-120k mi). I've never had anything except japanese cars, but some of my friends have had mercury's & other cars like that & have had many problems with them. I do not think that that is a coincidence. I'd recommend a Toyota Matrix or corolla or even a yaris. With honda, a 2004 civic or something like that. Best of luck.
"We are only as sick as our secrets"
Last December I paid 10k for a used 02 Honda Insight with 34k miles.
I have averaged 65 MPG, and it now has 52k miles.
It is an automatic (CVT).
I would look at the used Sentras of the current model. You might find a nice one in your price range.
Look at the Cunsumer Reports frequency of repair records for best choices, and compare that with higher depreciation on models other than Honda or Toyota.
I don't think the reliability of Honda and Toyota is nearly as good lately as it used to be. Also look for cars made in Japan, instead of the USA or Canada.
I would not sell your Chevy if the only problem is bad mileage. Might be something like a bad 02 sensor, or another relaitviely simple repair. If so certainly not a reason to dump an otherwise reliable car if it is in good shape.