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Using insets changes surrounding geometry.

The issue is that whenever insetting I or Extrude + Scale (E+S) the surrounding geometry changes.

Is there a way to accomplish this task without effecting the look of the surrounding mesh (or at least make it seem that the surrounding geometry belongs with the rest of the geometry).

I've attached some pictures:
click to enlarge

initial, no insets

enter image description here

adding insets

final with insets

In the pictures notice how everything is smooth in image 1 but by image 4 the surrounding areas after the inset seem like something was modified. Now if I want to extrude that little section in image 4 inside the mesh and create a cave, the surrounding mesh will just look weird.

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    $\begingroup$ you need more geometry. subdivide the mesh before insetting. $\endgroup$ – user1853 Dec 20 '16 at 17:09
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Whenever you have an object you want to smooth by adding geometry you should always try to work solely with quads (which you are doing right). However, vertexes which have more than 4 edges connected will result in an uneven smooth.enter image description here

Topology like the image below is better but still not perfect. It really depends on what your end use is. You, can add more or less sharpness by inserting 'edge loops' closer or further from the borders (which only works with good topology). enter image description here

A better way going about modeling this would be something like the following image: (not perfect but should help you get on the right path) enter image description here

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