Chattanooga has a fairly young craft cocktail scene but that doesn't mean you can't still find a great cocktail here if you look a bit.
Matilda Midnight
Matilda is a darling little bar inside the mid-century modern gem The Dwell Hotel. You can get an interesting cocktail and tasty small nibble. If you want dinner you need go no further than Terra Máe also located inside the hotel.
The Social Bar inside the Public House
The Social Bar is a popular happy hour gathering place in downtown. In addition to cocktails and great food it also has an extensive whiskey list and whiskey club.
Alleia
If you want a hearty rustic Italian meal with an interesting cocktail menu choose Alleia. They may have the coolest candleabra I've ever seen.
Chattanooga Whiskey Company
They even have their own local whiskey. Opening in 2015 it is the first legally distilled local whiskey in over 100 years. If you don't have time to stop by the tasting room you can try their whiskey in most of the local bars. But if you have a chance to stop by it's worth the effort.
Bonus
The Hanged Man Cocktail (photo on this page) was designed by a mixologist named Matthew Lawson. He is no longer at Matilda Midnight. But you can find him on Instagram as @ohmygodmatt seek him out, tell him I sent you and see what magic transpires.