I located a few additional details Dublin directory listings on the hotel you mentioned which might be of interest :
Pettigrew & Oulton 1834, Joseph Armstrong, Anglesea Arms Hotel , Crofton Place, Kingstown
Pettigrew & Oulton 1840, Alexander & Edward Armstrong, Anglesea Arms Hotel , Crofton Place, Kingstown
Thom’s Directory 1845, George Rathbone proprietor Anglesea Arms Hotel , Crofton Place, Kingstown
[a Mrs. Armstrong and a Richard B. Armstrong are listed on the same street]
Thom’s Directory 1848, George Rathbone proprietor Anglesea Arms Hotel , Crofton Place, Kingstown
The town of Kingstown is in south east county Dublin, the town built up after the construction of the large refuge harbour in the early 1800s, the name has now reverted back to Dún Laoghaire.
Based on the fact that the marriage appears on the index of Dublin Diocese* Marriage Licenses I presume your Armstrongs where Church of Ireland ?
* The Diocese of Dublin included all of county Dublin, along with most of the parishes in county Wickow and a few in County Kildare - about 160 parishes in total.
The are some transcripts of the Church of Ireland parish records for the Churches in Kingstown and Monkstown parish on RootsIreland, but these only have marriages back to the 1840s & 50s, the official parish for the area was Monkstown, which has baptisms, marriages & death/burial records going back to the 1600s - the historic records for the parish are held by the Representative Church Body Library in South County Dublin, as far as I know the records for this parish are not available online on any of the commercial websites at the moment.