Where is my minecraft server's spawnpoint?

I have a small public vanilla minecraft survival server, and I've decided to build a structure by the spawn point and increase spawn-protection within the server.properties files to prevent it from being griefed.

How can I find the exact coordinates of the centre of the spawnpoint. I understand from the minecraft wiki page, that the spawn point will be within a few hundred units away from the map origin (0,0), but as I'm only looking to protect a small area around the spawn point (say 128 blocks), I want to find the exact centre so I know where I should start building?

Alternatively, can I globally change the spawnpoint for all new players? I tried the /spawnpoint command, but despite not specifying a username, the response suggests that I've only altered my own spawnpoint. (i.e. "Set Bryan's spawnpoint to x,y,z")?

For info, I'm the server owner, and have full root shell access.

The exact co-ordinates of the spawn point are stored in the level.dat file. You can use an NBT editor such as NBTExplorer to find these values.

In NBTExplorer, go to File → Open... and navigate to your world folder. Open the level.dat file inside. Expand the Data entry and you'll find your SpawnX, SpawnY, and SpawnZ values, which you can then /tp to.