What is the ideal place to build a mob spawner in a survival world?
Since you are talking about 128 blocks, I'd assume you're already familiar with the spawning rules, but for others finding this topic, hostile mobs which are further than 128 blocks from a player will rapidly despawn, even though they can spawn anywhere in a 240x240 square from each player. There is also a cap on the total number of mobs which can be spawned at once, which means that if you have many people in different locations you may hit the cap, reducing the grinder's efficiency.
What this means for you is that the important thing isn't so much where your mob grinder is, but rather where the person running it is standing, and where others on the server might be causing mobs to spawn without being killed. To deal with the first, make sure that there are no legal spawn points outside your grinder within 128 blocks of where a person would be standing that would be "running" the grinder. Placing that person at y-level 128 would mean that you need to light up all caves underground, so a safer choice is to put their standing point at around ground level y + 128. You can also completely clear a 128 block square in the ground and build your grinder inside, if you want, or any other combination of tactics that results in no viable space being available for mob spawns within 128 blocks of the player that are not in your grinder. An ocean would partly solve this, since hostile mobs can't spawn in the actual ocean, but the caves underneath would still have to be dealt with or be out of range.
To combat the second, there is only so much you can do. On a private server with only a few people, you shouldn't hit the mob cap, but on a public server the only thing you can do is try to prevent mobs from spawning around players in your base. Generally, this means lighting all caves in the immediate area around your base, and possibly the ground as well if you want to maintain efficiency overnight.
Note that all of the above doesn't actually matter that much for basic mob grinders, since most of their inefficiency comes from having to wait for mobs to actually enter the killzone through random pathing, or through actually being killed by a player. It starts to become noticeable with grinder designs that actively kill the mobs as they spawn.
I should also note that I assume that you mean a mob grinder when you say a spawner - if you actually mean a monster spawner, the strategy becomes quite different since they have very different spawning rules from regular mob spawning.
Mobs spawn in dark areas. It's best you build a cobblestone room with no light source in it. You can build a spawner everywhere, even at a ocean. You might want to build that spawner very high above the ocean. Unless you want to make a spawner underground, it doesn't matter where you want to build it, so go ahead and put torches underground, unless you're building the spawner there. Digging at any layer underground works, so bedrock is a good idea.
Above ground:
Underground [Mind the torches, they're just to show the entire area otherwise you wouldn't see how big it is]:
