Looks like you missed a few closing tags and you nshould have "http://" on the front of an external URL. Also, you should move your styles to external style sheets instead of using inline styles.
.box{
float:right;
}
.box a img{
vertical-align: middle;
border: 0px;
}
<div class="box">
<a href="<?php echo "http://www.someotherwebsite.com"; ?>">
<img src="<?php echo url::file_loc('img'); ?>media/img/twitter.png" alt="Image Decription">
</a>
</div>
As noted in other comments, it may be easier to use straight HTML, depending on your exact setup.
<div class="box">
<a href="http://www.someotherwebsite.com">
<img src="file_location/media/img/twitter.png" alt="Image Decription">
</a>
</div>