Archer Tower at Town Hall 8: 5 of them, max level 10. At Town Hall 18 the cap is level 21. Max level per Town Hall, with how many you can build in brackets: TH3 3, TH4 4 (2), TH5 6 (3), TH6 7 (3), TH7 8 (4), TH8 10 (5), TH9 11 (6), TH10 13 (7), TH11 15 (8), TH12 17 (8), TH13 19 (8), TH14 20 (8), TH15 21 (8), TH16 21 (8), TH17 21 (9), TH18 21 (9).
Tap a Town Hall to open this item there. Dashed: not available at that Town Hall yet.