What are the specs on your computer? What video settings are you running GTA3 at?
Assuming you are running at the lowest settings on GTA, I know of a few things that may help. You can copy the audio files from the CD to your hard drive (check the website to get the directory locations) which is supposed to improve performance on some computers. You can also defragment your hard drive, which may help. (go to My Computer, right click on your hard drive and select Properties, then the Tools tab). Also, download the newest drivers for your video and sound cards.
In GTA itself go to the display menu in Options/Display setup. First make sure ‘trails’ is set to off; they slow the whole thing down horribly. Also drop the resolution a notch and lower the draw distance. That will probably help a bit.