http://elinux.org/CI20_upstream is probably the place to start.
I've only used the A10, which is $42, but single core, no flash, no analog audio jacks, and for some maddening/expensive reason, 0.05" headers, instead of the 0.1" on the A20.
It's a little behind the bleeding edge of Linux (still at 3.4), but I've been able to port an app from a beaglebone black to this with virtually no headaches. In fact, it's been nice, since there is no device tree at 3.4. Best of all, it's readily available, unlike the BBB.
http://www.raspberrypi.org/a-birthday-present-from-broadcom/
From the embedded GPUs VideoCore IV is as far as I know thus the most open (but rather the one-eyed among the blind).
I've been wanting to do stuff with MIPS instead of ARM, but this board won't be it.
Is that enough?
It's memory map is a little different. (For MIPS32 at least, not sure what KSEG of MIPS64 looks like) 80000000-9FFFFFFF is fixed to a cached view of the first 512MB of physical memory. A0000000-BFFFFFFF is fixed to an uncached view. Everything else is only accessible by mapping it via the MMU (both from a physical and virtual context). Last I played with MIPS cores, they were only soft fill TLBs, but maybe that's changed. Thumb2 is more expressive than MIPS16 IMO (but that's just, like, my opinion, man).
Other than that, the microarchitectual differences between individual implementations greatly outweigh the influence of the ISA, but for an in order design at least you can probably make a MIPS that'll compete well with an ARM for less transistors.