Generate better looking correlation table

Grid

ClearAll[labeledGrid]
labeledGrid[cs_: "GrayTones", is_: {80, 80}, 
  sty_: Directive["TR", FontSize -> 16, Black]] := 
    Module[{tbl = Map[Item[Pane[Style[If[NumericQ@#, NumberForm[#, 2], #],  sty], 
       Alignment -> Center, ImageSize -> is], 
       Background -> If[NumericQ@#, ColorData[cs][(1 + #)/2], None]] &, 
     Prepend[Join[List /@ #2, #, 2], Prepend[#2, ""]], {2}]},
    Grid[tbl, Dividers -> {All, All, {{1, 1} -> False}}, ##3]] &;

labeledGrid[][ccm, mem, FrameStyle -> Gray]

labeledGrid["Rainbow", {50, 50}][ccm, mem, FrameStyle -> Gray]

ArrayPlot

ClearAll[labeledArrayPlot]
labeledArrayPlot[cs_: "GrayTones"] :=  Module[{epilog = 
      MapIndexed[Text[Style[# /. x_?NumericQ -> Round[x, 0.01], 
          Directive["TR", FontSize -> 16, Black]], #2 - .5] &, 
       Reverse /@ Transpose@ Prepend[Join[List /@ #2, #, 2], Prepend[#2, ""]], {2}]},
    ArrayPlot[ArrayPad[#, {{1, 0}, {1, 0}}, White]  , 
     ColorFunction -> ( ColorData[cs][(1 + #)/2] &), 
     Epilog -> epilog, ##3,
     ColorFunctionScaling -> False, Mesh -> All, ImageSize -> 1 -> 80]] &;

labeledArrayPlot[][ccm, mem]

SeedRandom[1]
mat = RandomReal[1, {7, 7}];
labels = StringTake[#, 3] & /@ RandomWord[7];

labeledArrayPlot["Rainbow"][mat, labels, ImageSize -> 1 -> 50]

How about using MatrixPlot?

epilog = MapIndexed[Text[Style[Round[#, .01], 10], #2 - 1/2] &, Transpose@Reverse@ccm, {2}];
ticks = Transpose[{Range@Length@mem, mem}];

MatrixPlot[ccm,
 Epilog -> epilog,
 FrameTicks -> {ticks, ticks, ticks, ticks},
 PlotRangePadding -> None,
 ColorFunction -> (ColorData["GrayTones"][(1 + #)/2] &),
 ColorFunctionScaling -> False]

Readapting my answer here: DensityPlot with text

dim = Dimensions@ccm;

temp = Transpose[{mem}~Join~Transpose@Round[ccm, .01]];
table = Prepend[temp, Flatten@{"", mem}];

background = 
  Join[{None, 
    None}, {Flatten[
     Table[{i, j} -> ColorData["GrayTones"][table[[i, j]]], {i, 2, 
       1 + dim[[1]]}, {j, 2, 1 + 3}], 1]}];

Grid[table
 , Frame -> All
 , Background -> background
 , Alignment -> Center
 , ItemSize -> All
 , Spacings -> {3, 4}
 , ItemStyle -> {{Directive[Black, Bold], Automatic}
   , {Directive[Black, Bold], Automatic}}]