Use data from ajax to create an input in Laravel

I think your problem is working with HTML instead of JSON, and also you should consider working with templates instead of implementing HTML code inside your PHP code. This is going to be a long answer, please bear with me.

First of all you should switch your JS code to a proper AJAX call.

<!-- index.blade.php -->

<form id="search_form">
    {{Form::text('search_table', Input::old('search'))}}<br />
    {{Form::text('search_column', Input::old('search'))}}<br />
    {{Form::text('search_input', Input::old('search'))}}<br />

    <button id="search_button" type="button" class="btn btn-default">
        Search
    </button>
</form>

<div id="search_results" style="display: none;">&nbsp;</div>

<script type="text/javascript" src="/bower_components/requirejs/require.js"></script>
<script type="text/javascript" src="/js/global.js"></script>
<script type="text/javascript">
//  My testing system uses require, just use jQuery as you used to.
require(["jquery"], function($) {
    $("#search_button").click(function() {
        $.ajax({
            url: '/test',
            type: "post",
            dataType: "json",
            data: $('#search_form').serializeArray(),
            success: function(json) {
                // Just use json.data so we can add more details if we want to.
                if (json.data) {
                    /**
                     * Actually you don't have to addClass to your div, you can
                     * just show or hide it when you don't need it.
                     */
//                      $("#search_results").html(json.data).addClass('panel callout radius');
                    $("#search_results").html(json.data).show();
                }

                // Let's give feedback to user that they have gone off route ;)
                if (json.error) {
                    alert(json.error);
                }
            }
        }).always(function(xhr, status, error) {
            console.log(xhr);
            console.log(status);
            console.log(error);
        });
    });
});
</script>

I created a controller for you, you can change things to your needs.

<?php
// TestController.php
use Illuminate\Database\Eloquent\Collection;

class TestController extends Controller {

    public function getIndex() {
        $layout = View::make("test.index");

        return $layout->render();
    }

    public function postIndex() {
        /*
         * Sorry for shortening the code, you can just fix it as you go.
         */
        $f = Input::all();
        $rules = [
            'search_table' => 'required',
            'search_column' => 'required',
            'search_input' => 'required',
        ];

        $validator = Validator::make($f, $rules);
        if ($validator->fails()) {
            return \Response::json(['error' => 'You have to fill all the fields.']);
        } else {
            /*
             * We have a global array called $f now.
             */
            $term = str_replace(" ", "%", $f["search_input"]);
//          $search_results = DB::table($f["search_table"])->where($f["search_column"], 'LIKE', "%" . $term . "%")->get();

            /*
             * I created a result just for testing.
             */
            $search_results = new Collection();

            $results = [
                ['id' => 1, 'street_address' => 'Baker Street'],
                ['id' => 2, 'street_address' => 'Abbey Road'],
            ];
            foreach ($results as $result) {
                $newRow = new Collection();
                $newRow->id = $result["id"];
                $newRow->street_address = $result["street_address"];

                $search_results->add($newRow);
            }

            /*
             * Now comes the tricky part.
             */
            $layout = View::make("test.results");
            $layout->results = $search_results;

            return \Response::json(['data' => $layout->render()]);
        }
    }

}

Now we can create a layout for our search results. You can create a form inside this file, add checkboxes, form fields and etc, with some cookies and some Session using you can make the page remember what you have searched for and do more tricks.

<!-- results.blade.php -->
@foreach ($results as $result)
<a href="/some/url/{{$result->id}}">
    {{$result->street_address}}
</a>
<br />
@endforeach

in the routes.php file you should add;

Route::controller("test", "TestController");

These should do the trick for you I guess.

Best of luck!