Thank you all for your most helpful replies, in addition to an old picture in the Emmet story contributed by Shane.
It now appears that St PETER'S was demolished but it was in the St STEPHEN'S GREEN district, about halfway in a direct line between St PATRICK'S CATHEDRAL and St Stephens Green.
In the 1912 map also supplied by Shane, the street to its west is shown as WHITEFRIARS Street, and there was also a CARMELITE convent adjacent. But now having located its former location, in a more modern map, that part of Whitefriars Street is now shown as PETER ROW. Leading off this, towards St Patrick's Cathedral, is PETER STREET.
So, without doubt this is an ecclesiastical area of very long standing and the name PETER is lasting well after the church.
What sent me to this is a discovery at IrishGenealogy of some baptisms at St Peter's in the 1840s. I now think that there may have been more that are not showing at that site and am therefore keen to get to the RCB Library "one day".
Again, many thanks to you all for pointing me to what I needed to know.
Bill
Sydney