Nicotine is oily. Dawn dish liquid with warm water should work. Krud Kutter would work. Any good degreaser should do the job.
Ammonia and vinegar will make it just start running off.
Mean Green is the best thing I found.
I would try Bar Keepers Friend on anything stainless. I have used it before in the restaurant business back when people could smoke inside in Michigan. It works great and may help.
Good Luck! Lauren - The Little Lake Cottage
20 Mule team Borax
CLR works well.
I used Purple Power to clean the 8-foot grill hood in an old diner my nephew got. I swear it had never been cleaned! It took me about 4 hours and was not difficult. I tried many other things before the Purple Power and barely cleaned a few square inches. Make sure you use gloves; this is a very powerful degreaser.
When I'm cleaning a new clients house that smokes, I buy a gallon of Awesome Orange at the Dollar Tree, it melts that stuff right off. I also buy the large car sponge, and a pair of the rubber kitchen gloves as its hard on the hands.