Another way:

c:\@Work\Perl>perl -wMstrict -le
"for my $s (' bElLmOnT NY', ' NeW yOrK NY', ' sAuLt StE. mArIe MI',) {
   my $t = $s;
   my $name = qr{ [[:alpha:]]+ [.]? }xms;
   $t =~ s{ \b ($name) (?= \s+ $name) }
          {\u\L$1}xmsg;
   print qq{'$s' -> '$t'};
   }
"
' bElLmOnT NY' -> ' Bellmont NY'
' NeW yOrK NY' -> ' New York NY'
' sAuLt StE. mArIe MI' -> ' Sault Ste. Marie MI'
[download]

This takes advantage of the fact that a city name or portion thereof looks like a state/provincial zip/postal code abbreviation (but not an ISO one, apparently). See  \u \L and their friends  \U \l \F \Q \E in Quote and Quote-like Operators.