Tobacco Road (Downtown) - Not only is it the oldest bar in Miami, but their happy hours from 4-8 features 98 cent beer and well drinks. Which is absurd. This place has been a speakeasy, a strip joint, a gay bar, a gambling den, and Al Capone used to go all the time apparently. But he doesn't anymore, so don't be scared, just go there and pay one dollar for a drink and get an annoying 2 pennies back.
Monty's Raw Bar (Coconut Grove) - This place still holds a place in my heart (even though it doubles as a sauna). From 4-8 all their drinks are half off, which just means from 4-8 their drinks are reasonably priced.
Tapas y Tintos (Miami Beach) - I haven't been here, but they refer to their 6-8 drink specials as happy hours! Thank you! 2 for 1 drinks! Live music! Happy hours!