First, I have to refer you to this page on the CleanMPG site:
What if you cannot afford a “new” fuel efficient automobile? This may help.
I recognize it's not very pc to refer you outside this site but... It's a good article addressing just about exactly the topic you raised.
I suggest you post a blurb promoting standard transmissions for drivers who can drive a standard or are willing to learn. It's a decision a buyer makes only once and then must live with. Many are very unaware of the fuel economy penalty that comes with an automatic transmission.
I have to point out that much of the discussion on this site is on the topic of "adjusting the nut behind the wheel". That is, driving technique. The other major topic here is vehicle modifications. There are quite a few things one can do to help increase fuel economy which are both legal and safe.
Yes - Honda Civic VX and HX very good candidates. I'm considering an HX for my next car - though my current '89 Volvo may well go another 50 - 100 K miles before it gives up the ghost. The VX/HX were versions of the Civic that were tweaked for better fuel economy than the others. HX ('96-'05) was always a coupe, and the VX ('92-'95) was always a hatchback.
There will be other cars that are just about as fuel-thrifty as a Civic - but most of them will sacrifice something in safety or reliability. Or they're priced much higher, as in hybrid. Corollas might be a contender but there's more activity in modifications and do-it-yourself with Hondas than Toyotas. I think that's why you'll see lots of Civics discussed here.
Another truism is that the car you own now could well be the most economical - because you already own it. When you need to replace it for whatever reason, the fuel economy of the replacement can be a major consideration. Using the calculator in the previous post you can see how/why you might save only a few hundred $ a year by buying a gas sipper. Of course if your current vehicle is only getting 15-20 mpg and you're driving a lot of miles, then the calcs will come out to more savings.
You can use the calculator to compare keeping your current car with buying another. Just enter the current car's mpg and the "initial cost" as zero.
[Edited by BP for brevity - you should see how long this post was originally!!]