Anyway to change href of link with no id and no jquery?

window.onload=function() {
  var links = document.links; // or document.getElementsByTagName("a");
  for (var i=0, n=links.length;i<n;i++) {
    if (links[i].className==="checkout_link" && links[i].title==="Checkout") {
      links[i].href="someotherurl.html";
      break; // remove this line if there are more than one checkout link
    }
  }
}

Update to include more ways to get at the link(s)

document.querySelector("a.checkout_link"); // if no more than one
document.querySelectorAll("a.checkout_link"); // if more than one

to be even more selective:

document.querySelector("a[title='Checkout'].checkout_link"); 

Lastly newer browsers have a classList

if (links[i].classList.contains("checkout_link") ...

window.onload = function() {
  alert(document.querySelector("a[title='Checkout 2'].checkout_link").href);
}

<a href="x.html" class="checkout_link" title="Checkout 1" />Checkout 1</a>
<a href="y.html" class="checkout_link" title="Checkout 2" />Checkout 2</a>