The issue is really a Linq issue here and not a WP7 one. The query makes an anonymous type when you do the select new { ... } statement. This is not the same as the List<string> return type for the method.
You might be able to try changing the query like this...
public List<String> ge()
{
var r = from c in db.Favourite_tbls
join o in db.Menu_tbls on c.fk_menu_id equals o.pk_menu_id
select new String(o.menu_name);
return r.ToList();
}
You could also make a class that just had a string in it and use that as well. If you want a sample of that let me know.