Rosemary-infused lemonade is super delish. Something about the acidity draws out the rosemary. Lavender in lemonade would also be good.

Margaritas are a great, safe way to start mixing herbs with your cocktails because -- quite frankly -- they are very forgiving about your proportions. Add (1) a healthy amount of tequila, (2) at least 1 fresh squeezed lime or 2 of they are small/dry, (3) a touch of simple syrup or agave syrup, (4) and any one of the following muddled* combinations:

Green apple and rosemary (just a sprig for scent, do not muddle)
Cucumber and cilantro
Watermelon and thai basil
Blackberry and mint

Or, if tequila isn't your thing and your feeling all "pacific northwest," I had a heavenly Alpine Martini at a Belltown establishment several years ago. If I'm not mistaken, this is the recipe:

Mix 1.5 ounces citron vodka and 1 scoop of Douglas Fir Sorbet (recipe follows) in a chilled martini glass with 1 small cedar frond as garnish.

For the Douglas Fir Sorbet:

1 cup water
1 cup sugar
8 inches Douglas fir (cut into 1-inch lengths)
1 cup water
1 tablespoon gin

Boil first cup of water with sugar and Douglas fir for 10 minutes. Strain and cool. Add second cup of water and gin. Churn as directed on your ice cream machine.

A basil gimlet was possibly the drink that started me learning and experimenting more with cocktails. It could be made either like a mojito typically is with the basil muddled with simple syrup and fresh lime juice (as an aside, I much prefer these with simple and fresh lime as compared to Rose's lime) before adding gin or, as I did at home, was to make a basil simple syrup (simply steep the basil in a 1:1 sugar:water combination) to shake with the lime juice and gin. My wife, who was pregnant the last time I made the basil simple, enjoyed the basil simple and lime with seltzer for a non-alcholic alternative.

Mint is great in drinks other than the mojito too. The mint julep is an obvious one, but a gin-gin mule is a another great drink that uses mint, which my wife also enjoyed sans the gin. Look up Audrey Saunders' recipe for both the gin gin mule and the homemade ginger beer (which is super easy to make). If I recall, they are on the epicurious site.