me and my nephew were playing splitscreen and have been digging down in random spots.
A good spot we found was right behind the building with the lever (jail as we call it) dig straight back. Eventually we hit a little open spot with water. We went back a little ways and started digging down. Anyways we found all sorts of good stuff down there. You should give it a try.
I've always followed the rule of "Dig a 2x1 pit straight down to the Bedrock, and then go up TWELVE blocks from the Bedrock layer, and start digging in a straight line in any direction" method. I've found forty Diamonds in the Tutorial seed this way. However, the easiest spot I found was actually in the Village (with the Castle).
I went to the area SnizMasterJ is talking about... only I went into the little "abandoned mine shaft" in the building next to it. Notice that little patch of Gravel that just screams "DIG HERE!!!!!"? Yeah. Do that. Dig around in there, following my above method, and have your "Straight shaft" leading towards the Village. You should be able to find Diamonds around there.
Not a problem. If I'm able to, I should take screenshots to show you WHERE these "mythical diamonds" are hidden. Having me just tell you through text "dig here" isn't as helpful, I know... but my method of getting screenshots isn't working at the moment.
There's another spot for grabbing diamonds, but it seems sketchy (too random). If you go to the location of the furnace (the one next to the wall, placed there to demonstrate how to use it), and go behind it (as in walk to the other side of the wall) and take ONE BLOCK space ~left~ of the Furnace, and then take FIFTEEN BLOCK spaces forward, you should be either to the left of a tree (they seem to also spawn randomly) or near that tree, and facing the wall surrounding your spawning area (with the pond to the right). Dig STRAIGHT DOWN for a bit (chances are you will fall into a "cave" area) keep digging down (assuming you fell into that "cave" first) and you'll land almost right on top of a Zombie Mob Spawner, in a dungeon with TWO Chests (with Saddles, Cocoa Beans, and sometimes Buckets and Iron... but that's random). There is an underground waterfall in that area... usually there will be a 2x1 section of Diamond blocks near the source block.
However, again, it's random. It is the same cave system that I found some twenty diamond blocks (and eventually leads you all the way under the Village and Castle, and to a Skeleton dungeon). So explore around there, and you might find your diamonds even faster, than going under the village's abandoned mine.
Even with the same seed in use, diamonds do seem to have very random spawn locations... the only way you'll be "sure" of finding Diamonds is to search your map between layers 4 and 13 (the ideal layer being 12, which is why I suggest digging straight down to bedrock, and then going up twelve blocks and "branch mining" a location). So even if you had "diamond hunters" join you, it could be hours before you find any.
People believe that finding lava, also means you WILL find diamond ore... but this isn't true. Lava can spawn between layers 0 through 85 (but most commonly between 4 and 10, so really, you'd need to look UP two layers above lava, for your diamond ore)... so it's not a good method of finding diamonds. You're better off looking for Red Stone ore, because it shares the same layers... if you find Red Stone ore, you are going to want to keep searching that layer, for your diamonds.
Be warned, I don't think the tutorial level has any sugar cane. May be irrelevant to you, but I just thought I'd let you know before you started getting too far.
Oh, I know... and Steve, from 4J Studios, even confirmed that until the coming updates, you can't find Sugar Cane on the tutorial world... it made me sad at first... but I realized something... unless we get spells/potions/enchantments... the ONLY thing Sugar Cane is good for, that I can't "get" is food items. Once Pistons are added, I can make a complex "Gank!" system, to move the bookcases from the "Sanctuary" in the castle, to where I want it.
Now... if we were given the speed potions, I'd NEED Sugar Cane desperately... but that's not for months, if ever.
The Tutorial has two dungeons, clay, and everything else... so I can live without Sugar Cane. ^_^