Codice HTML:
<html>
<head>
<script type="text/Javascript">
function timesx(next,obj) {
var date = new Date();
var b = date.getTime();
next = next * 24 * 60 * 60 * 1000;
date.setTime(b+next);
obj.value = date;
}
</script>
</head>
<body>
<select name="add_giorni" onchange="timesx(this[this.selectedIndex].value,document.getElementById('newd'));">
<option value="30">30 gg</option>
<option value="60">60 gg</option>
<option value="90">90 gg</option>
<option value="120">120 gg</option>
</select>
<input type="text" value="" name="newd" id="newd" />
</body>
</html>
http://www.w3schools.com/jsref/jsref_obj_date.asp
EDIT: Ricorda che con javascript otterrai la data dell'utente, non quella del server. Altrimenti dovresti integrare php..