The previous owner of my 2002 was a smoker...
I had great success in cleaning the vinyl headliner with an excellent product called "Spray Nine". I bought it at Canadian Tire and have also seen it at Wal-Mart here in BC, Canada. It is marketed as an all purpose cleaner but is especially suited to plastics and vinyl. It is also a disinfectant. I also use it on things like my computer keyboard and phone, etc. I used Fantastik once (on another car) but it is too harsh and made permanent streaks on my windows where I did not wipe it off right away.
Use a medium-soft bristle brush to get into the grain and use plenty of clean rags so you do not just wipe the dirt around from one area to the next. I worked in small sections at a time so that there was no chance the cleaner would dry out before I removed it. Be careful around the window seals, they give off major black dirt unless they happen to be brand new.
It was a lot of work but it made my car seem new inside!
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