The "best" that you're going to find for that price point is a Pentium G. pcpartpicker.com has the G3258 (3.2 GHz, $62.10), G3450 (3.4GHz, $64.99) & G3420 (3.2GHz, $67.84). Primary difference is that the G3258 can use DDR3-1333 RAM, while the G3420 & G3450 can use DDR3-1600 RAM. For all 3, though, you have a dual-core processor with no HyperThreading, so they're more of a "budget" CPU than a true "gaming" CPU.
Cheapest core i3 is the i3-3250 or i3-4160, both for $99.95 on pcpartpicker.com.