We actually have so many, but the ones that are nationally known would include (going roughly from north to south):
・道産子{どさんこ} - Hokkaido
・水戸{みと}っぽ - City of Mito, Ibaraki Prefecture
・江戸{えど}っ子{こ} - Tokyo
・浜{はま}っ子 - Yokohama
・浪速{なにわ}っ子 - Osaka
・土佐{とさ}っ子 - Kouchi Prefecture
・博多{はかた}っ子 - Fukuoka
・薩摩隼人{さつまはやと} - Kagoshima (male only)
・おごじょ or 薩摩{さつま}おごじょ - Female version of above.
・うちなんちゅう - Okinawa (This is what Okinawans call themselves. They call us non-Okinawans やまとんちゅう)
As seen above, many demonyms use the old names of the areas rather than their current names -- 江戸、浪花、土佐, etc.
New arrivals:
・シロガネーゼ - Women of Shirokane area of Tokyo. Borrowed from "Milanese" in Italian.
・アシヤレーヌ - Women of Ashiya, Hyougo
・ニコタマダム - Married women of Futakotamagawa, Tokyo
***Answered by an 尾張{おわり}っ子 (western half of Aichi Prefecture)