This is a tough question, sort of like wanting your cake and eating it too. Generally, the quieter fans don't move much air. The louder fans usually run at a higher RPM in order to increase the air flow. However, the larger the fan is (greater blade area), the more air it will move, assuming the RPM is kept constant.
For example, my old P-III has a GlobalWin FOP heatsink. Originally, I used the 60mm Delta screamer 38 CFM fan, but the noise drove me crazy. Worse than my exwife's nagging. I replaced it with an 80mm Sunon high output fan that flowed 42 CFM. The 80mm replacement fan was much quieter and moved 4 CFM more air.
Ok, so the secret to a quiet CPU cooler is to find a good efficient heatsink and mate it with a really LARGE fan that runs at a low RPM speed. Specifically which one that is, I really don't know. Most of the quiet P-4 coolers I've seen are not that much better than the Intel retail cooler.
I think the Swiftech coolers are still the best available, but they are not quiet and cost considerably more than your budget. I've heard good things about the Volcano socket 478 cooler (don't remember the model). I've also heard that Alpha has a good heatsink that can be modded to accept a larger fan.
That's the key I think, using a larger fan. Most P-4 coolers, including the Intel retail cooler, use 70mm fans. Using a good 80mm fan will significantly improve air flow without increasing the noise. Even an Intel retail cooler would show improvements with the following cheap mods: 1) lap the heatsink, 2) use Arctic Silver thermal paste, and 3) replacing the 70mm fan with a better 80mm fan.