I just bought an 05 Neon
 

Recommend me some things I can do to help improve gas mileage.

Anything from $0-$500 MAX. Anything is appreciated.

Don't speed!

welcome, good to see another carolina guy on here. one thing is a scangauge. this will tell you what your mpg's are in real time and also give you a trip mpg meter as well. this will tell you when you are really sucking the juice. also after you get the scan gauge (retalis for $170 or so) you can look into a grill block. this is where you block off part of your grill to increase aerodynamics and allow your engine to heat up faster. it is good to do this after you have the scangauge because you can monitor your coolant temps.

other things people are doing include: increasing tire pressure to tire wall max, adding makeshift skirts for the rear tires, adding belly pans, removing side view mirrors, poping it into neutral going down hills, cutting off the car going down hills, adding elaborate boat tails for aerodynamics.

the first and foremost thing (which is free) is driving style. keep your rpms low and your car in the highest gear and that will do wonders.

I am sure there are more things but I would (and did) start with the scangauge

*edit* disclaimer: some of the stuff may be borderline legal (ex. side mirrors) so check your local laws about what is and isn't legal before doing things that are way out there