Wikipedia

Vacuum energy is an underlying background energy that exists in space throughout the entire Universe.

Clearly the vacuum energy has not been measured everywhere. Can I assume the vacuum energy is more or less constant everywhere, or is it possible some places have a different vacuum energy than other places?

You can reduce the vacuum energy in small gaps between conductive surfaces. That gives rise to the Casimir force. But otherwise, being the same everywhere seems to be a reasonable assumption. Pointless, in a way, since you can't tap into it.

I know you can't tap into it. I was reading about the vacuum catastrophe, and wondered if vacuum energy is different in space, distant from a gravity well, around a black hole, etc.

It depends on the system. For example a vacuum has a pressure gradient near sources of mass.

 

However on sufficiently large enough scales it uniform in distribution.

 

Ie there is no pressure gradient on cosmological scales.