If youve got a good motherboard and know how to overclock you can reach 4.5GHz even with a 30$ cooler.Still though it'd be running hot and noisy.
There are 3 coolers around that price that you should really consider.All of them are high-end to top-end air coolers.
The first one is the Tiniq Tower 120 Extreme.http://www.newegg.com/Product/Product.aspx?Item=N82E16835154011
It's cooling performance is as good as a Corsair H100 at low.And it also makes almost no noise.It provides the best accoustic effiency of all three.
The second one is the Zalman CNPS9900.http://www.newegg.com/Product/Product.aspx?Item=N82E16835118074
It's a huge top end cooler that looks awesome.It's cooling performance is phenomenal but it does get a bit noisy when the fans spin at high RPM.
The third cooler is the well known Cooler Master Hyper 612 PWM.It's the smallest of all three.Its also the only cooler that actually fits your budget
.Its pretty much does everything the Tuniq cooler does but a bit worse.It does have one upside though.Its more likely to fit in your case.