I've talked before about how there are certain cocktail "templates" that I use as starting points for playing with new ingredients -- why not tell you what they are, instead of just leaving that ellipsis? These are not all the classic cocktails, nor is this a true cocktail family tree -- there are good cocktail books out there that could tell you more about cobblers and fizzes in things. This is just the information in my head that I refer back to when I'm screwing around.
The Whiskey Sour
2 oz whiskey
1 oz lemon juice
sugar (I do it by sight/taste - just like with lemonade, the right balance varies for everyone, and every lemon)
sprinkle sugar in glass; dissolve with 2-3 dashes of bitters (including a dash of orange bitters) and a little ice water
add 2 oz whiskey and an ice cube
coat glass with absinthe, leaving just a little in the bottom
sprinkle sugar in glass; dissolve with 3-4 dashes of Peychaud's bitters, an optional additional dash of Angostura bitters, and a little ice water
add 2-3 oz rye whiskey
The Trinidad Sour
1 oz Angostura bitters
1 oz orgeat (a syrup)
3/4 oz lemon juice
1/2 oz rye whiskey
The Last Word
2 oz rye whiskey
3/4 oz sweet vermouth
2 dashes bitters (sometimes I leave them out if the vermouth is Punt e Mes)
These are templates. Think of using them as like parodying a song. When you take something out, you replace it with something with the same meter. You don't have to stick with that -- that's just where I start, and sometimes I tinker after that.
So if you take the lemon juice out, you replace it with another sour ingredient. Is there a Bloody Mary to be had using the Whiskey Sour template and a tomato/vinegar combination? Who knows! Maybe.
When you take out a liqueur, you replace it with another liqueur. Take out the liquor, replace it with another liquor.
For instance: use tequila instead of whiskey, triple sec instead of sugar, and lime instead of lemon, and a Whiskey Sour becomes a Margarita. The Aviation, the Blue Moon, the Daiquiri, and the Sidecar are all in the same family. Similarly, there are Last Word variants using every other base spirit in place of the gin, and they're all great (rye is a particularly good choice). I've mentioned this before, I think. It's important to remember, if you want to screw around with your bar.
So if you get a new base liquor, you can run it through all of the above and see how it performs. A new liqueur? Try it in Sour and Last Word variations. A new potable bitter/amaro? Sub it for all or part of the Campari in a Negroni, or for the Chartreuse in the Last Word.