I am in the process of creating a website. Currently the website has a solid white background with black text. However, on different monitors the white background can be blinding bright. I have attempted to changed the background to a more off-white color but it still can be bright. What are some techniques or ideas that are considered good UX design to help minimize this blinding white screen but not having a dark or black background with white text?
It's the contrast between your background and foreground colours that matters. So most things that will reduce this contrast while still having the text readable will help.
Personally, I like having an off-while subtle texture as the background and dark grey text for the foreground. This is still readable and easy on the eyes.
I agree with JohnGB, the contrast between your foreground and background will determine the legibility of your website.
However, your question seems more of a monitor problem than a specific UX question. All monitors are different and users have different levels of tolerance of the brightness set on their screens.
For example, UX StackExchange is mostly white with blue/black text. I have no problems reading it on my monitors with the brightness set to max.
So I wouldn't make these changes because "you" think it's too bright on "your" monitor. I would do some research on similar sites or conduct some tests with your audience to determine that.