This is a very mature mine, so I've done a lot of decorating and the actual mining takes place very far away.
Entryway -- it is a large 40ish by 40ish half-dome building with glass all the way around. The floor sits at y=10 and the dome rises up to about y=25, I think. In the center, a circular pipe made of lime concrete that is big enough to surround a 3x3 square rises up to the surface, on a fairly isolated island in a large lake. Acacia trapdoors form a grating on the surface end, and a single water column falls from the center. The water column passes through the floor and collects in a small retention pond that gives me access to the lava/bedrock level. The floor is occupied by a 3x3 arrangement of 17-block-wide diagonal platforms (they are one block bigger than the flow pattern of a single source block on flat terrain). The middle platform, which is located under the pipe, is floored with glass while the surrounding 8 platforms are floored with glazed terracotta. The pathways between the platforms and bordering the walls are made from brick stairs and slabs to prevent mob spawns, allowing me to focus the lighting on the platforms. The platforms contain a large pile of resource blocks (iron, gold, redstone, etc) with chests hidden throughout to store the extras.
The Undercity -- I chose to go for a circular quarry mine, expanding forever outwards from the entry building. The Undercity is organized along a spider's web of circular platforms at different y-levels with multitudes of staircases, elevators, and other things connecting them enough that I can essentially go in any direction in a straight line regardless of what height I want to get to. The buildings are fairly haphazardly strewn along the web, but they are distributed in a way that maintains a convenience storage of all building blocks so that I do not have to go back to Entryway to restock. The Undercity is otherwise mostly for decoration so I can have something neat to look at from Entryway.
The Ringwylde -- this is where all the mining takes place, and this is by far the most annoying part of the build. It consists of diamond-shaped platforms similar to how I store resource blocks at Entryway, but there's a LOT more (I did this just to use up the space, as the equivalent amount of chests wouldn't take up as much room). The Ring spans about 30 blocks, leaving me room beyond the trash-block platforms for a little wilderness decoration. Every 30 blocks cleared I build a new Ring and tear down the old one, adding in more spiderweb for the Undercity to grow into. When I'm feeling bored, I'll hop into the exposed caves and explore.
In addition to the spiderweb platforms, I've also developed a rail network to send back the blocks I've collected.
Mine aren't anything fancy as I value function over form, especially for something that will only be used for a few hours after the start of a new world (all the resources I need later on come from caving for fun, which meets my meager needs many times over, even with the fact that I have to use resources to repair my gear); my mines are just a large rectangular array of tunnels with a staircase leading down from my starter base just below the surface (not visible here as I dismantled it and filled it in, but I left the mine intact); the most notable thing is the fact that I make them below lava level but that actually isn't a big issue (I do this due to mods; the mine in my first world is at y=11):
This is a layer-by-layer cross-section, the lowest layer is y=1, above a single layer of bedrock, as this is from a modded world with an extremely rare ore (a few can be seen near the bottom as purple spots) which effectively replaces diamond and is most common at y=1 (due to this, the mine is also 2-3x bigger than if I used diamond; I found 91 diamond ore, several times what I'd need for my "caving gear"). Despite being below cave lava level and caves being more extensive than even vanilla 1.6.4 I didn't have many issues with caves/lava (I just mined through most of them after converting lava to obsidian). The lack of pockets where ores used to be is because I used excess cobblestone/dirt/gravel to fill them in, saving inventory space (I use quartz to build my main base, which itself was a byproduct of mining it for the XP):
This is a larger view of the area around the mine; I could have extended it a lot further east without running into many caves (there are more and denser/large cave systems in 1.6.4/modded but there are also larger cave-free areas due to a greater variation in local cave density):
These are in my Alpha 1.2.6 mod, but you can adapt them to modern vanilla.
First is my linear mine. I dug this out with TNT (just like in current versions, my TNT drops everything) and then decorated a bit. The pillars are a natural formation from the way I stuff my TNT into boreholes. It's 2 charges per section, top and bottom. I push the cart along to hold drops. After about 300 blocks, the tunnel turns and loops back.
This is a new wide-area "quarry" style mine I'm experimenting with. It's single charges of TNT, which (due to my borehole style) make a nice set of pillars and arches. I tidy them up, add some details and lighting: