Someone told me about this and I had to check it out... happy hours at Palomino's are actually fun and quite reasonably priced. My friend and I got $4 drinks which included all kinds of mixed cocktails and buy one get one free deal on pizzas and appetizers. We actually didn't spend that much and ended up leaving pretty full - no need to have dinner.
The restaurant is split into two sections - the bar has high and regular tables with a view on Fountain square. There is a separate area for diners and you can partially see the kitchen from there.
Lots of people come to hang out after work for drinks throughout the work week.