Have Snap to Point =ON. Disable all other snaps!!!!!
Insert a new anchor point to the wanted place of the circle center if there happens not to be one. New anchors can occur only on a stroke if the stroke is not an edge of a closed path. They can also have inner and outer strokes which are more complex cases.
You get it easily to the crossing of two lines if you have Smart Guides =ON
In theory you could place the circle also by relying on Smart Guides, but it fails easily if the board has already many other shapes. You get too much false indications from Smart Guides. For example it would be very difficult to place the center of the green circle exactly to the crossing of the red and orange lines if there was no anchor inserted:
So, Insert that new anchor point. Select the circle. drag it from its center. Hold Ctrl -key to get the direct selection tool into use temporarily. The center snaps to the node and gives a clear indication.
Useful to know: If you select your all black guidelines and apply Pathfinder panel's Outline every line will be splitted at every crossing. You get to the crossings anchors automatically. The lines become a single group with no color:
You get the color back by selecting the group and applying a stroke color. The number of line splinters can be high, but you manage them easily because they are a group.
It's useful to lock the group to prevent moving it accidentally. It has a drawback: If you place a circle center to a crossing like presented above you will not get very clear indication which changes temporarily the anchor color. But snap to the point happens anyway.