You might want to consider taking your Integra to a good 'ol boys suspension shop and have them go over the entire suspension and see what was done right and what was half-a**ed. A properly lowered vehicle, while often sportier in ride than OEM, should not ride like bricks unless done incorrectly. Also, 19" wheels with what I'm guessing result in somewhere around 30-series onion skins are hardly capable of absorbing much, so the ride quality will be compromised.
Danase brought up another good point- rollin' on huge honkers might sound fun, but adding weight and rolling resistance to the most crucial rolling component of your car has twice the resulting negative effects. Your braking distance as well as wear will be greatly increased without proper pad/caliper/rotor upgrades. Also, your fuel mileage is likely to suffer (is your speedometer off also?) Good luck!