Here are a few of the first chess clubs, in chronological order, up to the 20th century. Most have disbanded. I tried to list the founding date and the disbanded date if known.
Naples (1610), Café de la Regence (1670-1916), Café Procope (1689-1740), Slaughter’s Coffee House (1692-1843), Dublin (1749-1750), Salopian Coffee House (1770-1861), Parsloe’s (1772-1825), St James in London (1774), Paris near the Palais-Royal (1783), Berlin (1803-1847), New York (1803-1804), London (1807-1865), Zurich (1809 to present), Dusseldorf (1812), Hereford (1812), Dublin (1813-1819), Athenaeum in Philadelphia (1814), Manchester (1817-1876), Dublin Philidorian Chess Society (1819), Amsterdam (1822), Edinburgh (1822-present), Paris (1823-1839), Winterthur in Switzerland (1822), Percey Coffee House (1823-1825), Rotterdam (1823), Gliddon's Cigar Divan (1825), St Martins (1825-1827), Dundee (1826), Philadelphia (1827), Hyderabad (1828), Madras (1828), Samuel Reiss’s Grand Cigar Divan (1828-1833), Breslau (1829), Bristol (1829-1871), Nottingham (1829-1845), Hamburg (1830), Westminster (1830-1840), Cambridge University (1832), Trinity (1832), Berlin (1833), Covent Garden (1833-1840), Dublin (1833-1867), Simpson’s (1833-1903), Leeds (1834-present), Doncaster (1835), Federal City in Washington DC (1835), New York Divan (1835-1837), Norwich (1835), Cerce des Panoramas in Paris (1836), Exeter (1836), Greenwich (1836), Hambro (1836), Newcastle (1836), Pentonville (1836), St Petersburg (1836), Taunton (1836), Yarmouth (1836), York (1836), Liverpool (1837), Bassford's chess room in New York (1837), Wakefield (1837), Worcester (1837), New Orleans (1838-1840), Budapest (1839), New York (1839), Washington DC (1839), Glasgow (1840), Halifax (1840-1959), Huttman’s Garrick Chess Divan (1840), Norfolk in Virginia (1840), Brighton (1841), Belfast (1843), Huddersfield (1844), Boston (1845-1848), St George's (1845-1857), SG Winterthur in Switzerland (1846), Amsterdam Philidor Club (1847), Athenaeum in Philadelphia (1847), Birmingham (1847), Dundee (1847), Sheffield Athenaeum (1847), Penzance (1848), Burnley (1850), Newcastle-on-Tyne (1850), Shropshire (1850), Huddersfield (1851), Krefeld (1851), Leamington (1851), Melbourne (1851-1852), Brooklyn (1852), City of London (1852-1939), Edgbaston (1852), Shrewsbury (1852), Stourbridge (1852), Aberdeen (1853), Bradford (1853), Burton-on-Trent (1854), Dusseldorf (1854), St Petersburg (1854-1862), Tasmania (1854), Folkestone (1855), Great Northern Railway (1855), Mechanics’ Institute (1855), Ballarat (1856), McDonnell CC in London (1856), Yale (1856), Boston (1857), Croydon (1857), Milwaukee (1857-1883), St George (1857-1881), Vienna (1857), Dubuque (1858), Anderssen Chess Club in Philadelphia (1859), Auraria (1859), Charleston (1859), Denver (1859), Philadelphia (1859-1866), Social CC in Scotland (1859), Beverly (1860), Glasgow Central (1860), Leicester (1860), Victorian Club in Dublin (1860), Dudley (1861), St Petersburg (1862-1862), Wolverhampton (1862), Napier CC in New Zealand (1863-1870), Adelaide (1864), Georgetown in British Guiana (1864), Ladies’ CC in Germantown (1864), Ballarat in Victoria (1865), Copenhagen (1865), Rotherham (1865), Clerkenwell (1866), Melbourne (1866-present), Philadelphia (1866-1867), Westminster (1866-1875), Bury St Edmunds (1867), City and County Club of Dublin (1867), Press Club CC in Philadelphia (1867-1874), West Suffolk (1867), Bamberg (1868), Halifax (1868), Cornell (1869-1870), Oxford University (1869), Café Europa in New York (1870-1872), Caissa Correspondence (1870), Chicago (1870), Bristol & Clifton (1871), Cambridge University (1871), Newport in Wales (1871), North London (1871), Café Cosmopolitan in New York (1872), Athenaeum in London (1873), Augsburg (1873), Brighton (1873-1921), Buffalo (1873), Ibis in London (1873), City of London College (1874-1875), Germana in Berlin (1874), Harvard (1874), Kentish Town (1874), Philadelphia (1874-1877), Dunedin in New Zealand (1875), International Club in London (1875), Manhattan (1877-2002), Belsize (1878), Ludgate Circus (1878), Philidor Club in Brooklyn (1878), Rockford Female Seminary (1878), College Club in London (1879), Seattle (1879), Bournemouth (1880), New Orleans Chess & Checker Club (1880-1936), Acton (1881), Montreal (1881), south Norwood (1881), Stratford (1881), Hastings (1882), Kimberley in South Africa (1882), Moscow (1882), Rochdale (1882), St Leonard’s (1882), Warsaw Club in Kiev (1882), Bradford Exchange (1883-1884), Quaker City in Philadelphia (1883), Southampton (1883), Bridgnorth (1884), Brixton (1884), Golden Gate club in San Francisco (1884), Grafton in New Zealand (1884), Battersea (1885), British Chess Club (1885), Ealing (1885), Franklin Club in Philadelphia (1885-1887), Hampstead (1885-1955), Havana (1885), St Patrick's Club (1885), Baltimore (1886), Belgrade (1886), Helsinki (1886), Junior Club in Philadelphia (1886), Macclesfield (1886), Yorkshire (1886), Hobart in Tasmania (1887), Naples (1887), Colchester (1888), Ellesmere (1888), Franklin Club (1888-1893), Hereford (1888), Ironbridge (1888), Kington (1888), New Viennese (1888), Rathmines (1888), San Antonio (1888), Cheltenham (1889), Oswestry (1889), Leek (1890), Metropolitan Club in London (1890), Norwood (1890), Shrewsbury (1890), Staten Island (1890), Steinitz Club in Hawaii (1890-1891), Tacoma (1891), Wellington (1891), Pollock Club in Hagerstown (1892), Buffalo (1893), Franklin club in Philadelphia (1893-1955), Mannersmith (1893), Insurance Club (1893), West London (1893-1893), Women’s club in New York (1894-1949), Caxton Club in Brooklyn (1895), Cirenceter (1895), Exeter (1895), Ladies’ Club (1895), Steinitz Club in Philadelphia (1895), Blackpool (1896), Cosmopolitan Club in New York (1896), Knights Club in Brooklyn (1896), Milwaukee (1896), Exchange Club in Brooklyn (1897), Salisbury (1897), Atlanta (1898), Evans Club in Manhattan (1898), Gambit Room in London (1898-1958), St Petersburg (1898), Muswell Hill (1899).
References:
British Chess Magazine, "Chess in the Victorian Age," (1897)
British History Online www.british-history.ac.uk
Carolus Chess, “Chess Cafes and Clubs” http://sites.google.com/site/caroluschess/chess-cafes-and-clubs
Harding, “Which is the Oldest Chess Clubs?” www.chesscafe.com/text/kibitz184.pdf
The Chess Player’s Chronicle
The Chess Monthly
Wall, “Early Chess Clubs” http://www.chessville.com/BillWall/earlychessclubs.htm