Hi, BlueAthena! It is always nice to see another Elantra driver here.
First off, I'm glad that you have not tried to FAS (turn your car off while driving) your car -- that would be dangerous to the transmission. Most automatic transmissions do not deal with this well because they are lubricated by a pump that is run by the engine. When the engine isn't running, your transmission isn't getting lubrication. If you are still moving the gears will be turning and you'll have metal to metal contact. The short of it is you'd be looking at an expensive transmission repair or replacement in very little time.
It sounds as though you are off to a good start! I saw in another thread that you drive in the Atlanta area (challenging!

) so you'll have some extra challenges dealing with the congestion there.
Have you checked your tire pressure yet? They are almost certainly set at the Hyundai recommended pressure -- take those up to the maximum sidewall rating. It is perfectly safe but you will experience a slightly rougher ride. Advantages include lower rolling resistance (better fuel economy!!!), better traction in all conditions (dry, dirt, wet) other than in snow (and that is only marginally worse), better stopping distances, better cornering, and lower wear to the tire tread. Contrary to popular opinion, the tires will not "bulge" in the middle and have excessive wear there because the steel belts in modern radials will not allow that to happen. This is an easy update to do and will quickly net you a noticeable improvement.
Check to see if your car has fuel cut technology. This will turn off the fuel injectors if you are using engine braking and the RPM is over 1100. My car does not have it but since yours is 4 years newer there is a good chance you do. If you don't you'd be better off coasting to stops in neutral. In many cases coasting in neutral is a better option than engine braking anyway because you can coast much further and your average mpg can stay high over that whole distance.
Practice using DWL (Driving With Load) and DWB (Driving Without Brakes). The first one involves letting the vehicle slow down on uphills and speed up on downhills. The easiest way to approximate this by locking your foot in one position on the gas pedal. If you have any hills this will be more efficient than cruise control because you will use less gas going up hills. The second has to do with avoiding use of the brakes whenever you can. When you use your brakes you are sending some of your momentum away irrecoverably to heat from the braking surfaces. You used gas to earn that momentum and now you'll have to use more to get back to the speed you started wtih. Whenever possible leave large gaps (I know it is tough in the Atlanta area to do this!!) so that you can smoothly moderate your speed in response to traffic speedups and slowdowns without using the brakes and hopefully without changing your speed too much. Pick routes with lights in preference to ones with signs. You always have to stop at stop signs. Traffic lights can often be timed though. If you have to make turns on your trips try to choose routes that only require right hand turns. That way at least you have the chance to avoid stopping (think right turn on red).
Dropping your top speed can have a drastic effect on your fuel economy. Wind resistance goes up substantially as you get above 50mph and a good round number to keep in mind is that for most cars the most efficient speed is top gear at about 40mph. The closer you can get to that the better your mileage will be. I know you can't go that slow on the highway, but going slower (as long as it is over that 40mph mark!) will always be more efficient.
If you find yourself sitting at a light or other place longer than 10s, turn the car off. Most cars hit the break even point of using the same amount of fuel idling as they do restarting somewhere between 4 and 10 seconds. If the car won't move for longer than that time period you'll be saving fuel by turning it off and then starting it up again when you need to move. Along with that, don't warm up the car by idling it. Drive it gently until it is warm but do DRIVE it. Idling is 0mpg. Driving a cold engine won't be efficient but it is better than 0mpg!! Also, when you park, turn the engine off immediately. If you don't need to move, that engine should be off for the same reason as warm up idling! For parking, try to park "face out" so that you don't have to back up. Reverse gear is very low and extremely inefficient... and then there is the time that you spend stopped and then going forward. Added to the fact that it is more difficult to see obstacles when backing up, you are better off all the way around if you can just start the car and then put it in drive and go where you need to go. Parking on a hill facing downward is even better because then gravity helps you.
Coasting in neutral whenever possible can really improve your mileage a LOT. To get to where you can use that effectively you'll need to practice something called "rev matching" for when you put the car back into drive. To prepare, watch the tachometer and memorize the RPM for every 10mph increment. Then, when you are parked somewhere, practice raising the RPM of the engine to those set points with
GENTLE pressure on the gas pedal. The engine will rev very easily with no load on it. To use this, at speed you would shift into neutral to begin a coast. When you get down to a speed you want to be the slowest you are willing to go, raise the RPM to the correct level for the speed you are traveling, shift into drive again without moving your foot on the gas pedal, then continue driving as you normally would. This will prevent any harsh engagements of the engine and eliminate the possibility of undue wear on components caused by this procedure.
The above is going to take a lot of practice so be sure you try this out in a deserted area until you are VERY comfortable with it. Safety always comes first!!!
You may soon find (as I did!) that you no longer use the cruise control at all once you start mastering some of this stuff!
I know this was a very long response but hopefully you get something useful out of it! Don't try everything all at once -- you'll end up distracted, be more dangerous to other drivers because of this, and quite possibly get worse mileage because you aren't able to give the needed attention to all of the techniques just yet. Pick one or two and work at them until they become completely second nature to you. Then add another one or two. Eventually you'll be turning out numbers you wouldn't have believed even yesterday using all sorts of things you'll barely be conscious of doing.
Finally, if at all possible purchase a ScanGauge for yourself! It is very hard to get anywhere close to peak efficiency when you have to wait an entire tank to see if what you did had an effect. Over that period it is very difficult to tell what technique had what effect, too. With the SG you get instant feedback. I know it is expensive but it can quickly pay for itself if you are diligent about your efforts to save fuel. You drive enough miles that you could get that cost back very quickly indeed!
Good luck and stay active here -- we are always ready to answer questions!