I don't know about "tons of places" with super cheap happy hours; I guess it depends on one's definition of tons and super cheap.
There are plenty of places that will sell you a glass of wine or a beer at less than their going rate, along with $1 oysters.
And I'm sure there are a number of dive bars where a shot and a beer can be had for $5 or so.
But for instance, close to where you're looking, I like Porchlight, because you can get a properly made cocktail...here's their happy hour:
QuoteWHEN IS HAPPY HOUR?
Monday through Friday from 4pm-7pm. We serve three $12 specialty cocktails, $8 tall boy beers, and $6 flasks of punch.