Many rims I come across have this problem, while the rest of the wheel is fine (Nipple, spoke and rim are alloy, but for some reason metal part around spoke hole is not). What is the best solution for ridding this rust?

normally, oxalic acid would do a great job of removing spoke nipple rust, but in this case, the nipple is surrounded by the aluminum rim and galvanized spokes. oxalic will attack those two metals. so, there's no solution, really, other than to delace the wheel, replace/derust the nipples, and rebuild the wheel.

But wouldn't a chrome cleaner / polish should be harmless enough? No harm, I think, in applying a bit of Brasso, let it sit a while (five minutes?), then brush with an old toothbrush... worth a try?

I've found that a white vinegar soak + toothbrush works well. Fill a wallpaper wetting trough and do one section of the wheel at a time. Take the tire, tube, and rim tape off of there first, of course. I let mine soak overnight - so it took a few days to do them.
Spray some wax on there afterwards to try and prevent it from rusting again.

If you're just doing a surface clean, I'd go with some super fine #0000-steel wool or the little wire wheel on a dremel has been a great friend of mine for this sort of thing. I'll sit in a chair out in the barn with a wheel in my lap and go round one side with the dremel w/wire wheel, then flip it over and do the other side.

1-Soften it up with a squirt of WD-40 on each eylet.
2-WalMart Rust Remover 5.77/bottle, and a toothbrush or q-tips.
3-Apply liberally to each eyelet. If the Rust Remover sits too long on anodized rims, it'll lighten them up a bit, so be careful.
4-Usually 10 minutes will work. I often let it sit 5 minutes, then lightly rub with 0000 steel wool on each eyelet. BigPolishJimmy's idea of the dremel wire wheel would probably be quicker.
5-Two applications will generally take care of it. I put some of the rust remover in a small cup and use q-tips to get inside each eyelet (unlaced rims).

I've done two sets like that, working on a third, which was a lot worse. They eyelets came clean, and I'm slowly removing the ano with EZ-Off, then I'll "khatfull" the rim with varying grades of sandpaper and have polished rims, stainless spokes and polished hubs...on a $50 frame. But it's fun.