Immediately south of Government House [1], Stanley’s Sports Centre (Reservoir Rd., tel. 27291) includes a public swimming pool, but hours vary—phone ahead or ask the tourist office.
For fishing, the nearest site is the Murrell River at the west end of Ross Road, but the improved road network has made other East Falkland [2] sites almost equally accessible.
South Atlantic Marine Services (Ross Rd. and Dean St., tel. 21145, www.falklands-underwater.com [3]) rents diving equipment and does dive tours. In and around Stanley [4], shipwrecks, kelp forests, and reefs (with their sea lions and elephant seals) are great attractions for divers.
Links:
[1] http://www.moon.com/destinations/argentina/the-falkland-islands/stanley/other-sights
[2] http://www.moon.com/destinations/argentina/the-falkland-islands/east-falkland
[3] http://www.falklands-underwater.com
[4] http://www.moon.com/destinations/argentina/the-falkland-islands/stanley