You should take advantage of GeoDistance listability.

In[2]:= level1$dists = 
   GeoDistance[level1, level1, 
    DistanceFunction -> "Center"]; // AbsoluteTiming

Out[2]= {0.91751, Null}

Also with the default option is fast:

In[3]:= level1$dists2 = GeoDistance[level1, level1]; // AbsoluteTiming

Out[3]= {1.34659, Null}

But for a list as long as level2, you should do partition yourself and call GeoDistance in groups. Instead of using Partition, you can also use directly the natural partition of first administrative divisions, something like:

In[4]:= level2u = AdministrativeDivisionData[#, "Subdivisions"] & /@ level1;

In[5]:= level2$dist = Outer[GeoDistance, level2u, level2u, 1]; // AbsoluteTiming

Out[5]= {288.062, Null}