Alfheim svømmehall has a pool which is open weekdays between 15-21 and weekends between 10-16.
Charming communal swimming pool with a cosy gym, showers and sauna. Sauna included in swimming ticket. Check www.tromso.kommune.no/alfheim-svoemmehall.121163.no.html
If you want something to do inside on a rainy day, swimming might be a good alternative.