We are plagued with moles and I have just learned to co-exist with them. The lawn looks like a mine field most of the time, but oh well. I'm not a grass snob, and my lawn does not even remotely resemble a golf green - instead it is a mish-mash of field grasses, clover, daisies, buttercups, other weeds, and mole hills. The only way we have found to effectively get rid of moles is to trap them. As Porkpal suggests, flatten out the existing hills to get a notion of where the main tunnels are, then place your traps accordingly. I run around my lawn with the riding mower blade set at the lowest setting but without the blade on to flatten the hills. Sometimes I toss some reseeding grass seed over the smushed hills, but usually not.
My neighbor has good luck just gardening close to a new hill, and when she sees movement, she stabs straight down with her shovel and kills them that way. I don't have that patience.
My dog occasionally catches one, but actually makes as much of a mess as the moles do -- mole hill versus dog hole - you decide...
Otherwise, we've tried all known urban legends - Juicyfruit gum, human hair, castor oil, crushed eggshells, garlic, those silly whirly-gigs, super sonic vibration devices, peeing in, flooding, gassing the tunnels - no luck with any. I know my husband has also poured gawd-awful concoctions down the holes (I'm a staunch organic gardener, but he has a 'hidden' poison stash in the barn), and nothing he's come up with has worked so I'd advise against any chemical measures. All that does in my mind is poison the earth and put your pets at risk.
Good luck!
Edited: Cross posted with Greene. You referred to the whirly gigs as pretty, I called them silly. No offense intended. To each their own. I have no pink flamingos....