I don’t have a collection yet, so my one good whistle gets a lot of use. It’s nickel, and the fingerholes have been tarnished pretty well - as well as the two spots on the bottom where my thumbs rest. Scrubbing it with a wet cloth has worked, somewhat, but it’s a lot of work. Is there an easier way to get tarnished spots off a whistle?
Sure. Any low-abrasive metal polish or polishing cloth should work fine. Many people like Cape Cod or Sunshine cloths. I sometimes use an old rouge cloth for spots, or Simichrome for a rare all-over.
But really, other players expect to see exactly the tarnish pattern you describe. If a handyman shows up with all shiny, spotless tools, it kinda makes you wonder. 
I’m partial to a little patina on brass myself though nice to see it shine every now and then. Non of my nickel whistles tarnish and I do wish they would 
Hmmm … I haven’t come across a problem with tarnish on nickel. Silver, sure, and brass gets dull, but not on nickel. What does happen with a lot of nickel whistles is that the nickel wears off altogether, revealing the brass underneath. Any rubbing whatsoever, with however gentle a cleaner or cleaning method, will only increase the loss of nickel and expose more brass. If you think that your cleaning method has ‘improved’ it, it could just be that you’ve made the brass shinier and therefore blend in more with the remaining nickel.
What make of whistle is it? If we know the make, we can probably tell whether it is indeed a nickel plated whistle, plated on brass, and therefore whether my thought has any relevance.
BTW, I rather like the spots where the nickel wears off and you can see the brass underneath.
If you think of it as patina as opposed to tarnish, you’ll not mind it as much and may even come to embrace it. A well patinaed whistle shows that it’s been played a lot, and that’s a good thing.
Tarnish/discolouration/patina is sorta cool, shows that the whistle is a veteran and not a Johnny-come-lately. Like the saxes that many pros play.
It’s a Jerry Freeman Bluebird whistle.
Thanks for the answers, everyone - I’m not quite as bothered by it anymore, and I do love a classy amount of tarnish. I think I’ll try out the polishing cloths that MTGuru mentioned, but I’m sure I’ll come to love the look eventually - especially once I get a few more whistles to show which ones are veterans.
I have a nickel plated Gen Bb and a nickel silver Shaw D, and both will get some slight tarnishing after a while. I’ve found that the same rubbing alcohol and water solution I use to clean eyeglasses and other stuff around the house will also help clean/shine up the whistles. I’ve even used it on brass just to get the funk off from oils and sweat. (It won’t remove the patina.)
Yes, I have the JF Bluebird, nickel, and the finger holes & thumb rests are showing my whistle history… and I’m proud of it. 
“A picture is worth a thousand words” 
It’s not tarnish then - it’s the nickel wearing off. If you like the effect, stop cleaning it. If you don’t like the effect, stop cleaning it - it’ll wear even more nickel away.
Then again, just buy another Bluebird so you have both the historical and the shiny evidence that you play the whistle. 
I also have a habit of eating Dorittos during practice and I get a nice greasy tinge to the fingering holes. When I’m done practicing I just shake out the whistle a bit.
Ewww! Doritto grease in your holes!
Nobody ever asks for a go on my whistles. 
No. I get that.
Good idea! Don’t have to share that way!
I don’t share the Dorittos either.