Fuel-Efficient

Maybe you don't like them, but the Prius is the obvious automatic/CVT car that meets your criteria. Lots of them are available in your price range, they get better mpg, and reliability will probably be better too.

I don't know about the HX CVT (there weren't a whole lot of them made), but the hybrid CVT that Honda made at the same time for the Civic was very unreliable. I would do a little research and make sure the HX doesn't have the same reliability problems as the hybrid before considering a Honda CVT of that vintage. And in general the VW's of that vintage are relatively expensive to maintain.

If you're serious about maximizing mpg, a manual transmission would probably be the way to go; regardless of what the epa mpg's are. See the mpg data reported on this site or a lot of the ecomodder discussions. Another high MPG car is the Toyota Yaris.

This is the right time to buy a fuel-efficient car, since they're relatively cheap when gas prices are low.

Good point above on the Honda CVT. A manual is best for durability as well as real-world efficiency. Also a good point is that an HX CVT will be nearly impossible to find--a nationwide search on AutoTrader currently comes up with just one HX, and it has a manual transmission.

A 10-year-old VW isn't guaranteed to be unreliable, but the possibility is significant. The 2005 is the next-to-last year of the generation that earned VW its bad rep. It will be quieter and smoother than the Honda, though. It might be possible to find a 2009 Jetta TDI that meets your criteria. The main concern with these is that some owners report very expensive fuel system problems, but these might now be in the past. I'd check tdiclub.com for more information on the reliability of the 2009s.

So I agree that a Prius is likely your best bet. You can get a 2008-2009 with about 100k miles for $8,000.

If you'd prefer a Honda, the same money will get you a 2010, maybe even a 2011 Insight with fewer miles. But the Insight did nothing well, and quite a few things badly. I didn't like the ride, handling, noise level, performance, or seat comfort. Probably still worth checking out, as your impressions could differ.