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Thanks very much for the information. I did look here for any help but I found nothing https://archive.org/details/nycmarriageindex?and%5B%5D=year%3A%221916%22

Kevin

Those are the New York City records. They are kept separate from the NY State records

Google 1880s maps of San Francisco

Listed as Clary Street on this map - I think the map is wrong because Google Maps today calls it Clara St., but not positive. look for a few more maps and decide.
click on the link to enlarge
http://www.davidrumsey.com/maps1140049-30522.html

Lincoln grammar school not far away. don't know if kids were assigned by location back then as they are today, or if parents could send them wherever they wanted.

Google "were there high schools in 1883 in san francisco"

https://sfgenealogy.org/doku.php?id=san_francisco_county:databases:schools
https://www.foundsf.org/index.php?title=Public_Schools_in_19th_Century_San_Francisco
didn't look for part 1
has a section on Lincoln grammar school

https://en.wikipedia.org/wiki/List_of_oldest_schools_in_California

Afternoon,

I followed your links to Jeremiah & Sarah's wedding and then to Maria's marriage. I tried to search Ancestry/Family Search for US or NY Census showing Jeremiah & Sarah. I couldn't find one. I was hoping to see Maria, some siblings (hopefully William) and perhaps an address near the many I've identified for William & Cathering--unless you found it and I missed it in this chain?

BTW, if you look in William Sr's gallery you'll see a map I created of all the addresses I've identified to date.

The only records I have found for anyone named Sullivan married to a Sarah Simpson are the civil records in Ireland and Maria Sullivan's marriage to Robert Roundtree in NYC in 1881.

To make a positive connection to the couple who married in Cork City in 1851, you/we need to find a connection in the US between Maria and William - like a common address, or find the family with all children arriving together, or a baptism record for William S in Cork son of that couple.

edit to add:
I did find the map and locations. very helpful.

And for what it's worth, some city directories. I started at 1878 trying to match the 42 Cherry St address you say they were at on the 1880 census, but didn't find it. Also from 1892 and worked backward, but didn't quite meet in the middle. I didn't do whatever is available from 1884 to 1888.

New York city directories

1878 City Directory
William Sullivan, h 110 South Street probably the same man as 1889
no other Sullivans at that address. no Sheas or O'Sheas at that address

1879 City Directory
William Sullivan, h 3 Canal St
no other Sullivans at that address. no Sheas or O'Sheas at that address

1880 City Directory
William Sullivan, clerk 519 W 28th

1882 City Directory
William Sullivan, clerk, 408 E 85th

1883 City Directory
William Sullivan, clerk, 408 E 85th

1889 City Directory
William Sullivan clerk, h 110 South probably the same man as 1878
William Sullivan clerk, h 18 Varick

1891 City Directory
3 Wm Sullivan, clerk
  115 Washington Place <-- likely him
  890 Boulevard
  1384 3rd Ave

1892 City Directory
William Sullivan, clerk 18 Beach <-- him
other William Sullivans at   
  890 Boulevard
  1384 3rd Ave
  122 E 113th
  311 W 13th
?? Jeremiah O'Shea at 26 Beach
?? Margaret O'Shea, widow, 22 Beach

Assuming that is him at 18 Beach in 1892, then that eliminates 2 of the 3 addresses in 1891, because those men are still at the same addresses, leaving 115 Washington Place as the only possible address for your William in 1891. - assuming he was listed in the first place.

Best bets are the later ones at 18 Varick and 115 Washington Place.  And the 18 Beach Street address is where the child Elizabeth Sullivan was born in 1891, daughter of Wm Sullivan and Catherine O'Shea.

I have my doubts about the earlier addresses, but included them anyway.