Which AVR32 do you want to use ?
If it is the AT32AP7000 then the NGW100 board is probably the way to go though over your budget.
For the AT32UC3A and AT32UC3B, there are a couple here in your budget, though I did not try them :
http://alvidi.de/produkte_module_en.html
I have used the EVK1101.
Also I have used the 64 pin protoboard from Electroboards and fitted AT32UC3B0256. Added decoupling and xtal on protoboard. Then USB connector, 3.3V regulator, and two push buttons for reset on another board. Because the chips come with the USB bootloader as standard it works fine. A few hours work and some fine soldering, but under $20 !
The software framework and FreeRTOS from Atmel take a bit of getting used to due to its size and complexity. However it does work well and is great for USB device and host. The Device Firmware Update (DFU) bootloader is well integrated into the free AVR32 Studio.
The UBW32 using the Microchip 32 bit device may be an alternative for you.