Centering Bootstrap input fields

The best way for centering your element it is using .center-block helper class. But must your bootstrap version not less than 3.1.1

<link href="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/4.0.0-alpha/css/bootstrap.css" rel="stylesheet" />
<div class="row">
  <div class="col-lg-3 center-block">
    <div class="input-group">
      <input type="text" class="form-control">
      <span class="input-group-btn">
             <button class="btn btn-default" type="button">Go!</button>
         </span>
    </div>
    <!-- /input-group -->
  </div>
  <!-- /.col-lg-6 -->
</div>
<!-- /.row -->

You can use offsets to make a column appear centered, just use an offset equal to half of the remaining size of the row, in your case I would suggest using col-lg-4 with col-lg-offset-4, that's (12-4)/2.

<div class="row">
    <div class="col-lg-4 col-lg-offset-4">
        <div class="input-group">
            <input type="text" class="form-control" /> 
            <span class="input-group-btn">
                <button class="btn btn-default" type="button">Go!</button>
            </span>
        </div><!-- /input-group -->
    </div><!-- /.col-lg-4 -->
</div><!-- /.row -->

Demo fiddle

Note that this technique only works for even column sizes (.col-X-2, .col-X-4, col-X-6, etc...), if you want to support any size you can use margin: 0 auto; but you need to remove the float from the element too, I recommend a custom CSS class like the following:

.col-centered{
    margin: 0 auto;
    float: none;
}

Demo fiddle

Try applying this style to your div class="input-group":

text-align:center;

View it: Fiddle.