I put tire shine on my whole rim (I have black rims) & it makes the rims & tires look brand spanking new.
I used to just wash them with soap & water, they would look good wet but once they tried it looked like crap. Try using the actual "wheel & tire cleaner". Smells just like bleach pretty much, spray it on your rims and it'll turn it all brownish (that's all the dirt & grease being removed). Then through some tire shine on there and you're set! Like maybe $10 worth of product and 15min of work.