I had a similar problem (with a multi-dimensional set of distances between each pair, but I don't think that makes a difference). My solution was to use a "simulated-annealing" approach. A pseudo-code description would be something like

my @items
my @best_layout
my $least_error

for (0..100)
  {
    foreach @items
        add to layout at random x,y
    best_error_measure = sum of badness of all inter-item distances
    my $jiggle_distance = largish
    while($jiggle_distance > smallish)
      {
        randomly pick item try it in four alternate locations 
                (up, down, left, right)
        if(new_error_measure < best_error_measure)
            keep the item in its best new location
        else
            jiggle_distance *= 0.95
       }
    if(best_error_measure < least_error)
      {
        save layout into best_layout
        least_error = best_error_measure
      }
  }
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This has the advantage that you can take any consideration into account when measuring the "badness" of a layout, for example are there items you want near the centre. For my data it very rapidly converged on a reasonable solution (the optimal solution would have taken much longer but I just needed something that was "good enough").

For my particular data the standard "cluster analysis" approaches gave poor results, and I wanted a two dimensional display of the results.