Uncaught TypeError: Cannot read property ‘length’ of undefined

You are not passing the variable correctly. One fast solution is to make a global variable like this:

var global_json_data;
$(document).ready(function() {
    var json_source = "https://spreadsheets.google.com/feeds/list/0ApL1zT2P00q5dG1wOUMzSlNVV3VRV2pwQ2Fnbmt3M0E/od7/public/basic?alt=json";
    var string_data ="";
    var json_data = $.ajax({
        dataType: 'json', // Return JSON
        url: json_source,
        success: function(data){
            var data_obj = [];
            for (i=0; i<data.feed.entry.length; i++){
                var el = {'key': data.feed.entry[i].title['$t'], 'value': '<p><a href="'+data.feed.entry[i].content['$t']+'>'+data.feed.entry[i].title['$t']+'</a></p>'};
                data_obj.push(el)};

            console.log("data grabbed");  
            global_json_data =   data_obj;

            return data_obj;


        },      

        error: function(jqXHR, textStatus, errorThrown){ 
                        $('#results_box').html('<h2>Something went wrong!</h2><p><b>' + textStatus  + '</b> ' + errorThrown  + '</p>');
        }
    }); 

    $(':submit').click(function(event){
        var json_data = global_json_data;
        event.preventDefault();
        console.log(json_data.length);

        //function
        if ($('#place').val() !=''){
            var copy_string = $('#place').val();