It will depend on what your faucet (and drain cover) are made of. Maybe yours has a mirrored chrome finish or maybe it's a brushed nickel. It might be brass or stainless steel. It could even be plastic. Having hard water will not damage the drain cover like somebody pouring Liquid Plumber down the sink will and yes, people do that because they don't think. If you're buying one new, read the instruction manual. It will say which cleaners to avoid. Typically, I like to stay away from anything that contains ammonia, bleach, and usually alcohol. Also, I would not suggest using a Brillo pad / steel wool / Scotch-Brite or scouring pad when cleaning it. These days they make faucets with a PVD finish (atom-bonding) that can fade. If you use the cleaner on your floor or oven, don't use it on your faucet. You also don't want to use something like Scrubbing Bubbles or tile / shower cleaner or anything that says it removes rust and tarnish. Keeping it clean and free from build-up will make it easy to maintain with an ammonia-free cleanser and soft cloth. (Right now I'm using Method in an all-surface cleanser since my faucet has a satin finish but there are many different products available on the market and some you can make at home... keep reading....) If there is build-up, you can use a toothbrush and some liquid dish soap (they usually say to avoid detergents) or if that doesn't work you can also try Barkeeper's Friend which is a mild abrasive but I would test it first. You could also try a 50/50 white vinegar and water especially if you need to soak the nozzle to remove build-up. Keeping it clean and dry will prevent you from having to use a harsher cleanser to get rid of mineral build-up or water spots.
There is a book I really like called that is put out by Consumer Reports. It is called <a href="http://www.amazon.com/Practically-Anything-Editors-Consumer-Reports/dp/0890438439">"How To Clean Practically Anything".</a> It answers many-a-"how do I clean this"-question. Everybody should have this book handy, imho.
<img src="http://ecx.images-amazon.com/images/I/51YYQCXMVVL._BO2,204,203,200_PIsitb-sticker-arrow-click,TopRight,35,-76_AA240_SH20_OU01_.jpg" alt="" />
(My 16 year-old self is highly disappointed with what my interests have become.)