You'll be able to find lots online. Regarding the various Coleraine addresses- most of the centre has been vandalised by redevelopment but you'll be able to see most of it from Google Streetview.
Coleraine in Modern Times by Dr. Mullin and the Bann Disc (issued annually by Coleraine Historical Society) are most likely local histories.
(Primary) School records most likely to be in PRONI- you can check their e-catalogue. Coleraine Academical Institution (now merged with Coleraine Girls’ High School and called Coleraine Grammar School) had excellent records on past pupils and its pupils have had a long association with rowing on the Bann.
There are also directories that cover the period of interest-
1880- River Bann Rowing Club - Boat-house, Hanover Gardens. Wm. Price, treas.
LINK Other directories covering Coleraine on same site but I can’t see William Price listed under Customs.
Emma Price’s marriage in 1873 (St. Patrick’s Parish Church in the centre of Coleraine) gives her address as New Row-
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1873/11270/8133018.pdfhttp://colerainehistoricalsociety.co.uk/?page_id=22 Still New Row when daughter Harriette Lydia Price married in 1878-
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1878/11099/8062196.pdf Son William living Lodge Road when daughter Emma Stanley Price born in 1882-
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1882/02798/2026748.pdf Living Ballymoney Road in 1884 when son William Binden Stanley Price born in 1884-
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1884/02706/1996227.pdf Coleraine Chronicle, 14 Nov.1896: … scrutiny into the voting papers for the election of seven pupils was announced, Among these elected were—William B Stanley Price, son of late Br. William Price, draper, Coleraine, Lodge 754, 2,595 votes William H Winter, son of late Br. William Winter, hotel- …
Note: the 1882 & 1884 addresses might be the same place. The present Lodge Road crosses Lodge Road roundabout to become the road to Ballymoney (Newbridge Road) but I have seen it listed as Ballymoney Road.
Northern Constitution, 21 Nov.1885: KID DRIVING & HAND KNIT GLOVES. WELSH M … SCARFS, … LONDON FELT HATS, … WILLIAM PRICE, HOSIER, GLOVER, AND SHIRTMAKER CHURCH ST., COLERAINE.
Living Hanover Place when daughter Frances Grace Stanley Price born in 1887-
https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1887/02564/1948134.pdf Son William Price living Hanover Place when he died in 1888 age 41-
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1888/06162/4761252.pdfColeraine Chronicle, 15 Dec.1888: DEATH OF MR. WILLIAM PRICE, COLERAINE. We regret exceedingly to have to announce the comparatively sudden death of Mr. William Price, which took place at his residence, Bridge Street, Coleraine, early on Wednesday morning. The deceased gentleman was in …
The Will of William Price late of Coleraine County Londonderry Silk Mercer who died 12 December 1888 at same place was proved at Londonderry by Henry Anderson Macaulay of Coleraine Solicitor one of the Executors. Will dated 1882 mentions ‘dear wife’ and ‘infant daughter.’
https://apps.proni.gov.uk/WillsCalendar_IE/WillsSearch.aspx Widow Sarah & 2 children living Portrush by 1901-
www.census.nationalarchives.ie/pages/1901/Antrim/Portrush_Urban/Landdowne_Crescent/932240 www.census.nationalarchives.ie/pages/1911/Londonderry/Ballylagan/Glenmanus/595465 The Valuation Revision Books are also online free and you can see approx. when the family might have moved to and from various locations-
https://www.nidirect.gov.uk/information-and-services/search-archives-online/valuation-revision-books