Priceline for Heathrow?
 

Arriving LHR late at night, thinking about staying near airport the first night to save money and late night hassles getting to hotel I will stay in for the next week. I am staying directly on Picadilly line , so easy to get there from LHR but I risk arrive after the tube shuts down. Are the airport hotels easy to access... Do they all have shuttles? Or is this going to be a hassle unto itself.

I do not believe that the airport hotels have shuttles.
There is an airport (private) shuttle which will charge around 6 or 7 pounds per person. You can buy tickets at the airport.

We use Priceline all the time for overnights at Heathrow. I've never paid more than US$90 for a four-star hotel (usually one of the Sheratons, Marriott or Crowne Plaza.)

The only "free" shuttle I know of runs between Terminal 5 (British Airways) and the Hilton at Terminal 4. There's also a Sofitel connected (walkable) from T5, but it's very pricey.

There's a free bus zone that covers the airport and most of the hotels along Bath Road (A4) but arriving late at night, plus having luggage, makes that alternative unappealing. Otherwise, you're stuck with the Hotel Hoppa Bus, which charges £4 one way. There are several Hoppa routes, so you need to make sure your bus goes to your hotel.

Even with the Hoppa (which virtually every traveler through Heathrow comes to hate with unmitigated passion) the price savings you can achieve through Priceline can make for a very easy and relatively pleasant stay near the airport overnight.

Otherwise you have to take the Hotel Hoppa

Oops, sorry for the dangling Hoppa reference. My eyes cloud over when I think of that dreaded conveyance.

Thank you for your replies! When I went to check my outbound flight there had been a schedule change, including a 12 hour layover in Newark! Ack! I was able to switch to a nonstop to LHR arriving at noon which sounds perfect!

That's great - but for others reading this: Priceline is fantastic for LHR hotels. And as mentioned - there are no hotel shuttles. Normally the Hoppa or a local bus are the best options . . . HOWEVER neither works for a late night arrival.

The Hoppa stops running between 10:30 and 11:45PM - depending on the specific route.