One night London layover - into Stanstead out of Heathrow

You definitely don’t want to be anywhere near Liverpool station as it’s over 200 miles from London.
I assume you mean Liverpool St station - full names matter here.
Liverpool St is these days an ideal spot to stay over. Plenty of good hotels and restaurants in the immediate area and the opportunity to walk down to Tower Bridge if you want to stretch your legs. The following morning just take the new Elizabeth line straight to Heathrow.

If you stayed in the area of Liverpool Street station then you would be straight onto the Elizabeth Line next morning, at about 7am (so before the morning peak) for 8.15 check in for your 11.15 flight. It is a bit under the hour to Heathrow on the Elizabeth line.
That seems to maximise your time.
It's important to add the 'Street' bit on, if asking for directions, otherwise people might think you mean the city in the North of England!!

The SE also goes to Tottenham Hale allowing a connection into London via the Victoria line - so easy enough to go many places really. The Victoria line goes into King's Cross St. Pancras, where you could also connect to the Piccadilly line for Heathrow the next day. That's about an hour trip. But it would also make it very easy to head to many other options for the evening.

Just to throw it into the mix should you decide against the place you have found - Liverpool Street area works fine but so do a lot of other places.

Jill, I don’t know kings cross / Pancras well. Is it better to stay there then Liverpool street area? I don’t really know London well at all so if you think there is something specifically nice to hang out for the evening there I am all ears!!

Personally I wouldn't stay in that area but it is very popular - plenty of food and drink places, six lines into the King's Cross St Pancras Underground station.

It was more to highlight that you don't need to restrict yourself to the Liverpool Street area - using the Tottenham Hale link you can get to many more places in an extra 20 minutes or so. I know you don't have loads of time to play with but anywhere vaguely central is in reach and then easy enough to find an Elizabeth line or Piccadilly line link the next day with no or one change.

I personally really like the Pimlico area - also on the Victoria line.

I like the Kings Cross/St Pancras area and these days there are plenty of nice bars and restaurants behind Kings Cross.
But two things would sway me to Liverpool St for this. Firstly it would mean not making a change at Tottenham Hale. Secondly the Elizabeth line is a much nicer ride than the Piccadilly line for the day after, albeit more expensive - £13+ against £5.60pp. Pretty small fry against the overall cost of the trip though.

I decided to stay at Liverpool Street in the shoreditch area. Plan is to have dinner at Dishoom Shoreditch and if time permits walk around and look at street art which I heard is nice really cool in that area. Thanks for all the great advice!

I love it when a plan comes together

Well done Julie.

Nice spot for respite in Shoreditch is Oat Coffee. Liked it very much when I was there last year. Pleasant staff. Good strong coffee.