It depends on your seed for the best y: # that diamonds spawn at, and you wont know unless you "cheat". Diamonds generate at y: 0-16. Use F3 and start a branch mine at y: 12.
Why Y: 12? If you bring a water bucket, you wont have to deal with lava flowing into your mines. Lava pool generate at y: 12, so they will be on your mines floor, just use a water bucket on the block next to lava. Plus you spend less time dealing with lava, and more time mining.
They spawn randomly anywhere between Layers 0-16. There is no true "Sweet spot" for diamonds. Most players mine at y=13.6, because you're above lava, but can still encounter diamonds just as frequently as when you would mine lower.
Private Mod Note
Rollback Post to RevisionRollBack
If it's tainted, blow it up. If taint persists, blow it up again.
The curve is flat at just over 100,000 blocks, between 5 and 12.
Diamond doesn't spawn at a rate of greater than one node per chunk. I used to look at old maps with Cartograph G for diamonds, and from memory it is usually once every 2-3 chunks or so. Diamond is said to usually spawn near lava, but my experience suggests that lava's proximity is coincidental.
Recommended feet position is 8-10y, but the closer you are to 5 at feet pos, the better, since you can see more. The lava layer is generally 11y, but contrary to traditional opinion, mining below the lava level really isn't that dangerous, as long as you've got headphones on and are paying attention. Lava makes that much noise these days that you'll know you're close to it long before you actually see it.
Systematic clearing of chunks is also recommended, (use Rei's minimap to discover chunk boundaries, or you can find them at x or z co-ords which are evenly divisible by 16) which you can do efficiently using the One Chunk Branch Mine method that I normally use, and wrote about at that link. That method is efficient because it allows every block in a chunk at that elevation to be seen, while only mining out 45% of the chunk's total blocks. The reason why systematic chunk clearing is necessary, is because diamond nodes only spawn every 2-3 chunks, as mentioned.