The promenade is not far away and easy to access. We did our 'own thing' and had a lovely day going up the mountain on the cable car to the restaurants, park and visitor centre etc at the top, then the shops along the promenade on our return.
It depends where the ship docks but P & O normally have a shuttle running into the town near the cable car station, they do charge for this service I think. Doing it on foot is practicable but , hey, you're on holiday. ...Nei.
We have been many times to Madeira and there is either a free bus shuttle into town or a tender.
Caught the free bus into centre. Went up in cable car, came down in basket-not for the faint hearted! Then caught service bus to Camara de Lobos, small fishing harbour. Had lovely lunch in restaurant( Winston Churchill's)and stroll around harbour.Very relaxing day.