Very short London trip, hotel recommendations

[Tellmewho]

We live abroad and will be visiting family in England soon.

After our main visit, we will be travelling into Liverpool Street around lunchtime, and flying out from London City Airport the next day (late afternoon). In this very short trip, we are hoping to meet some old friends in central London for an afternoon and dinner together.

Can anyone recommend a cheap hotel (max £150 for family room inc breakfast) that is relatively central, but an easy journey from Liverpool Street /to City Airport?

This is local to me. Check out this place I found on Hotels․com!
hotels.app.link/vjdmj6fGyRb
I've not used the hotel (it's above a nice pub) but it's easy to get to central London and city Airport from Leytonstone. Or there's more choice in Stratford (Moxy) or a Travelodge opposite Snaresbrook tube.