As aldux suggests, a simple way of accessing JSON cross-domain is to use JSONP. In your case, the server (dailymile.com) does support JSONP, so you can simply add a ?callback=? parameter to your url, i.e.

var dmJSON = "http://api.dailymile.com/entries.json?callback=?";
$.getJSON( dmJSON, function(data) {
   $.each(data.entries, function(i, f) {
      var tblRow = "<tr>" + "<td>" + f.id + "</td>" + "<td>" + f.user.username + "</td>" + "<td>" + f.message + "</td>" + "<td> " + f.location + "</td>" +  "<td>" + f.at + "</td>" + "</tr>"
       $(tblRow).appendTo("#entrydata tbody");
 });

});