Preview is Not Remembering Window Sizes and Positions on Startup (after Update to High Sierra)
Preview does remember the position of windows containing images (JPG, PNG, etc) but for some reason does not restore the position of PDF windows. I suspect this is a bug.

The saved state for Preview is located at: ~/Library/Containers/com.apple.Preview/Data/Library/Saved Application State/com.apple.Preview.savedState

Meanwhile, you can use an app like Stay to remember and automatically reset the position of any window. It’s a bit heavy handed for this use case but it would let you carry on until the bug is fixed.

You might also look at window managers such as Tiles or Rectangle that allow easy manipulation of windows.