Start by pressing up the tires to 40 PSI or so - that's probably the easiest/cheapest/fasted mod. If you can get some sort of upper grille block on it, that'll REALLY help the warmup part. Depending on your commute, that could net you 2-3 MPG.
Be careful when you change oil on it! My 2.0L Elantra (2004) only takes 3.5 qts. I think the little Accent engine is only 3.25 - check the manual for sure.
Shift low, and get to 5th fast. Optimal acceleration *probably* starts around 2000 RPM. I'd shift no later than 2750 max; 2500 may be even better. Cruising RPM in the 1500-2000 range should help you keep the MPG up.
PANTS! You don't have a tach. RRRRRR...
1-2 shift at 8-10 mph
2-3 shift at 14-18
3-4 shift at 22-26
4-5 shift at 28-32
Those are rough guesses, but should be within 1-2 mph. I'm pretty sure you should be able to do 30-35 mph in 5th without lugging. It's near the bottom of the gear, for sure - probably 1200-1400 RPM.
Alignment may be a good idea - the default specs are almost zero on 'em.
Check out
Hyundai Service Website - it's practically the full shop manual for the car for free, from the manufacturer. PM me some time and I'll walk you through how to use it (can be a little confusing).
Does that have a serpentine belt or a 3-belt setup? If you don't mind Popeye steering, and it's got a 3-belt setup, you can pop off just the power steering belt and leave the others on.
First pic link wasn't working for me. I'll ask on the Elantra forum (we do all HyunKia, though) about a cluster swap for you.