Knowing the position of the next GUI Image

If you don't want to manage it yourself then consider adding all "circle" UI images to a single List and then just iterate through whole list and check ~like that:

     Image nextImage = null;
     Vector3 currImgPos = currImg.transform.position;
     //for going right:
     foreach (Image img in mylist)
     {
         Vector3 iteratedImgPos = img.transform.position;
         if (iteratedImgPos.y == currImgPos.y) //or allow some variation +/-
         {
             if (iteratedImgPos.x > currImgPos.x) //check if there is any circle on the right
             {
                 if (nextImage == null || iteratedImgPos.x < nextImage.transform.position.x) // check if any circle was already found to the right, if was check if that circle is closer
                 nextImage = img; //if not closer then next circle should be this one
             }
         }
     }
     if (nextImage != null) //if there is next circle to the right
     {
         //do whatever you like
     }
     else //if not
     {
         //do something else
     }
     //where currImg is your "current circle" and mylist is a collection of all available "circles"

Do pretty much the same for left, but instead you should check if next X position is lower. Same will do for Up/Down but instead you should check for equal X and higher/lower Y.

Though it will be better for performance to manage it yourself, for example it can be X:Y Map like multidimensional Array:

 bool[,] moveArray = new bool[10, 10];

Where True value represent a circle and false nothing, then if you want to move right you just check like this:

         if (moveArray[currXvalue + 1, currYvalue])
         {
             //i can move
         }
         else
         {
             //i can't move
         }

Else it can be managed with Tags which you can manually add to images, and so on.