Have been big for a decade but the ones I read about sound odious. I'm giving up my generation when I say that the only ones I can understand are a gin martini, a Rob Roy, and something from my youth that was called a Bootlegger: 1/3 gin or vodka, 1/3 grapefruit juice and 1/3 volume crushed mint, tossed in a blender with ice. Heavenly, but I recall making some rather bizarre decisions after several.
So, considering that I abhor sweet drinks, what's worth drinking today? No cranberry juice, please, or too much lime as I vaguely remember a grotesque experience with gimlets. Ah, and no Bourbon.
Again, nothing sweet.
Since you don't like sweet, I don't think a VC or Manhattan would be up your alley. Also, your stip that no bourbon may also mean that rye isn't your favorite either, but if you like rye, than a Perfect Manhattan or even a dry Manhattan are great. Most of the spinoffs are pretty damn good too (Little Italy, Greenpoint, etc.).
In summer, there's nothing better than a properly made Tom Collins or Gin Rickey or Gin & Tonic (with good tonic).
There's the Jasmine. The Negroni. Mentioned above - the Aviation. The Corpse Reviver #2. The Pegu Club.
If you like tequila, I recommend the La Rosita.
If it's rum, a Hemingway Daiquiri or a Papa Doble.
Kindred Cocktails and Cocktail DB are good resources if you don't have a bunch of cocktail books.