How to improve handling without lowering the ride height?

I guess gripy tires will do.

How about sway bars?

 

sway bars, better tires, performance shocks

 

Yep, what he ^^ said pretty much covers it. You could also consider springs and stiffer bushings in the suspension, but you start losing the comfort from the suspension real fast, so it's a direct tradeoff. If you wanted to go crazy, you could even go with coilovers, just not dropped though.

 

Lowering your car without roll-center adjusters makes your car handle worse, unless the factory designed the optimal suspension point lower than stock.

then as everyone said.

Basically tires are the biggest upgrade you can do by leaps and bounds.

After that, it depends on how much money you want to spend and what your goals are.

Free mod: inflate your tires. Hard to know to what point though without data logger. If you have iphone you can dl harry's lap timer and do skidpads somewhere safe. Overinflate your tires to like 40, then skidpad, then let air out in increments after letting the tires cool, re-test, etc.

If you want something simple, sway bars will work. They won't improve maximum traction and you may even get worse steady state traction, but it will be quicker in transitions and feel nicer.

If you have money, ideally roll should be controlled with the springs, not sway bars. New shocks/struts should help better than sways, assuming you get high quality spring/shocks. Most coilovers on the market are not high quality. And don't get beefy sways if you get coilovers.

You can get camber adjustable arms for the front and knock out your front camber to like -2 to -3, and your rears to the maximum negative you can get. Or you can get a tire temperature monitor and figure out your ideal camber.

New bushings will help, especially if your bushings are old or you decide to run sticky tires.

After that, if you get adjustable coilovers, you can corner balance your car with you in it while keeping height around stock.

After that, you can go find out the real proper spring rates for whatever streets/track you drive on, you can get custom springs then if you got something re-valvable you can send your shocks to someone to get it custom revalved for that spring rate.

There's also weight reduction.

And then aero, but i think any front splitter you get would have to be custom made, and it's not a good idea to put large rear aero without front.

Then at that point you might get some benefit out of chasis rigidity, like a roll cage.

Great reading:
http://farnorthracing.com/autocross_secrets.html

 

...or you could just replace all your worn bushings and shocks. It'll make your car feel 10x's better.

 

I also wouldn't buy gripy tires. They might get tired and start complaining about spirited driving.