Updated 14 Aug 2021
I decided to search on ancestry in 2018 in the US Federal Census 1870 , for all people recorded as having been born in Ireland (exact) and resident in a named State (exact). A word of caution here, the numbers are not always entirely accurate depending on search engine capability, the literacy of the enumerator, the accuracy of the transcription or indeed the report given by our ancestors to the enumerator. However, this list does give us some idea of the scale of the research necessary if we have been told that our ancestor settled in such and such a State.
A further word of caution for those researching the Brennan name, many Irish people were not literate in the English language and I have found many phonetic spellings for the name Brennan, some of them very amusing. The highest concentration of the Brennan family name in 1870, (According to ancestry) was in New York with 1,319 followed by Pennsylvania with 377.
Links below are free to view at familysearch once you open a free account.
Alabama 3,904 Irish born
Brennan (Exact) 1
Arizona 496 Irish born
Brennan (exact) 0
Arkansas 1,485 Irish born
Brennan (exact) 3
Upper Township, Sebastion, Arkansas
Amy Brennan 1844- (www.familysearch.org/ark:/61903/1:1:MNC6-R1W)
John Brennan 1835- (www.familysearch.org/ark:/61903/1:1:MNC6-R14)
Little Rock, Ward 1, Pulaski, Arkansas
Jack Brennan 1849- (www.familysearch.org/ark:/61903/1:1:MNC8-Y3T)
California 54,454 Irish born
Brennan (exact) 52
Colorado 1,685 Irish born
Brennan (exact) 1
Denver, Arapahoe, Colorado Territory
Michael Brennan 1838- (www.familysearch.org/ark:/61903/1:1:M4LK-M43)
Connecticut 70,473 Irish born
Brennan (exact) 215
Delaware 5.907 Irish born
Brennan (exact) 0
Florida 732
Brennan (exact) 1
Key West, Monroe, Florida
Michael Brennan 1832- (www.familysearch.org/ark:/61903/1:1:MNZJ-7F8)
Georgia 5,114
Brennan (exact) 5
Savannah, Chatham, Georgia
Michael Brennan 1835- (www.familysearch.org/ark:/61903/1:1:MCSP-838)
Bridget Brennan 1838- (www.familysearch.org/ark:/61903/1:1:MCSP-JNG)
Mary Brennan 1840- (www.familysearch.org/ark:/61903/1:1:MCS2-56B)
Thomas Brennan 1823- (www.familysearch.org/ark:/61903/1:1:MCSL-YQM)
Mary Brennan 1825- (www.familysearch.org/ark:/61903/1:1:MCSL-YQ9)
Idaho 989
Brennan (exact) 0
Illinois 120,308
Brennan (exact) 203
Indiana 32,070
Brennan (exact) 30
Iowa 40,359
Brennan (exact) 38
Kansas 10,963
Brennan (exact) 6
Kentucky 21,703
Brennan (exact) 14
Louisiana 17,143
Brennan (exact) 19
Maine 15,680
Brennan (exact) 6
Maryland 23,578
Brennan (exact) 10
Massachusetts 214,869
Brennan (exact) 250
Michigan 41,892
Brennan (exact) 52
Minnesota 26,390
Brennan (exact) 30
Missouri 54,988
Brennan (exact) 81
Mississippi 3,372
Brennan (exact) 0
Montana 1,645
Brennan (exact) 0
Nebraska 4,970
Brennan (exact) 2
Nevada 5,042
Brennan (exact) 2
New Hampshire 12,157
Brennan (exact) 11
New Jersey 86,792
Brennan (exact) 123
New Mexico 550
Brennan (exact) 1
New York 729,121
Brennan (exact) 1,319
North Carolina 693
Brennan (exact) 0
North Dakota 303
Brennan (exact) 0
Ohio 83,215
Brennan (exact) 85
Oregon 1,985
Brennan (exact) 2
Pennsylvania 238,466
Brennan (exact) 377
Rhode Island 25,387
Brennan (exact) 61
South Carolina 3,317
Brennan (exact) 4
South Dakota 743
Brennan (exact) 0
Tennessee 7,179
Brennan (exact) 5
Texas 4,041
Brennan (exact) 2
Utah 523
Brennan (exact) 0
Vermont 14,087
Brennan (exact) 12
Virginia 5,252
Brennan (exact) 0
Washington 1,057
Brennan (exact) 1
West Virginia 6,891
Brennan (exact) 1
Sheridan Magisterial District, Lincoln, West Virginia
Michael Brennan 1825- (www.familysearch.org/ark:/61903/1:1:MZ4L-LCK)
Wisconsin 48,592
Brennan (exact) 68
Wyoming 1,109
Brennan (exact) 2