Why are microtubules absent in and around the nucleus?
tl;dr Cells are 3D and the cytoskeleton does not exist within the nucleus.
There are several things you have to be aware of when looking at such pictures. Remember, you are looking at a 3D object which is not homogeneous and uniform in depth.
Shape of a plated HeLa cells
You are looking at HeLa cells. When plated like in your case, they adhere to the plate and make a generally thin, 2D-ish shape with lamellipodia (the extruded parts that look like they are grasping the plate on the sides of each cell). The nucleus is the most prominent vertically bulging part of the cell - the nucleus takes up most of the depth of the cell and there is little space around it. You have to appreciate the vertical dimension of the cell around the nucleus especially. The shape is a little like an egg cooked sunny side up; the yolk makes a bulge and the egg white is thinner around the yolk and there is little space for large filaments like microtubules. Remember, cytoskeletal filaments are so in size: small (actin) filaments &lt; intermediate filaments &lt; microtubules. This is exactly why you see more actin, a little less intermediate filaments, and even fewer microtubules exactly on top or below the nucleus in these 2D plated cells. Also, please remember that these cells are not representative of most cells.
The nucleus is a separate compartment
The nucleus is also a separate compartment, within which the actin and microtubule cytoskeleton system do not exist. The nucleus performs its own structure-keeping in the form of the nuclear lamina, which is composed of protein meshes that sit on the inner membrane of the nucleus.
You are not seeing the small actin filaments inside the nucleus, only around it. The microtubules are too large to see above and below the nucleus in most cases, since they are much larger filaments. In some cases though, you would see microtubules in HeLa cells above and below the nucleus.
See picture below: microtubule stain shown in green.

Other images for a more wholesome appreciation of the cytoskeleton.
Here follow a few micrographs of HeLa cells.
In green, actin.
In red, intermediate filaments stained with vimentin:

And now here you can see a microtubule stain in HeLa cells, in pink. Notice that some microtubules do actually make it around and across the nucleus.