It's a flat City so hire bikes, beach is away from the City 30 mins+ from the Cathedral. Walk up the Cathedral steps (free) for a panoramic City view, go to the city beach, beaches to the south are wild and practically deserted, great places to eat and drink. Carmen is an easy going neighbourhood (where I stay) but your teenage daughter might prefer Ruzafa, south of the station.
Bisecting the Cty is the Turia riverbed/park, there is enough in there to keep your daughter interested for a few days, Google it.
It's a great place, far more relaxing than BCN or Madrid.