My old burner died on me, so I'm looking to buy a CD-RW drive. I thought that it would be cool to get one that works very quickly with EAC, but I'm having a hard time.

For it to work well with EAC, it ideally won't have audio caching.

Is it possible to find a burner that
A) doesn't have audio caching
B) ideally 52X
C) less than $30 all said and done

I think most of the CD-RW drives now are shipping at 52x24x52 or 52x32x52 at around that price range, so I don't think you'll have difficulty finding one at that speed. The most common brands (like LG, Lite-On, Aopen) are retailing around here are in that price range. Seems like the market in my neck of the woods favours drives that are the cheapest rather than the newest and best. I have an LG writer (8520B) and am pretty happy with it. It handles DAE in secure mode quickly and hasn't given me grief when writing. The more exotic brands around here are Plextor and Pioneer which are DVD/CD-RW writer combinations. Plextor retails for around $150 ($C)
At the price you are spending I don't think you have to put too much thought into your decision. I would make one suggestion that might get you going in the right direction. Do a quick survey of your system configuration . Find out the model of your motherboard, CPU, memory, operating system, bus type etc and then google or search her in HA for similiar configurations that make references to EAC and CD-RW drives. You might get some hits that will reveal general problems.
In the end though, I believe you'll end up with a decent enough drive to handle your DAE needs in EAC.

I bought a Lite-On SOHR-5238S for about $25. A very nice drive for the price. Only complaint is that it doesn't do overreading (because I rip to lossless). It rips quite fast and can read many cd's my Plextor cannot. Blows right through copy protected discs, my plextor chokes on them. For the price you can't complain though. And in case it was obvious, it's a 52x drive.

EDIT: I'd also like to add that it rips about 4x as fast my Plextor PX-W4012A too.
EDIT 2: was mistaken about Lite-On drives caching, so I removed that bit. Still a fast ripping drive.

My SOHR-5238S does cache audio data (at least with the latest firmware).

Hey your right, sorry about that. I alway remember it not caching, but it does. It's still fast as hell in EAC for a caching drive with caching disabled. Must be my NEC dvd burner that doesn't cache, which is also cheap (about $40).