The hotel is a little ways out of town, but there is a courtesy bus, and also, the local bus service is fairly good--we used it a number of times. The hotel has an indoor pool, which is handy, because in June the outside one is still quite chilly. There is a gym, tennis, and bowls, etc., but it is very expensive, so we didn't bother. The only thing that seems to be free is swimming.
Opposite the hotel, there is a bakery/snack shop, and they will make up rolls if you need them at a reasonable price, and they're very tasty too. Every Saturday in June, you will be able to see the fireworks competition down at the harbour, which is fantastic, and the displays are put on by a different country each Saturday. Get there early, though, because it does get crowded. There are some great eating places down on the seafront--even a Pizza Hut if you fancy it. Try the garlic bread, which seems to be served everywhere - it is gorgeous! There are some fantastic gardens to visit. You can go up in a cable car to where the toboggans are, but we felt that they were a bit overpriced.
Quick Tips:
Madeira is quite hilly but the public transport seems to be fine so it is still possible to get about. If you're a dog lover, don't get stressed about the number of dogs walking about, they seem to be very streetwise and even use the crossings!
Santa Katarina Park is lovely to sit and watch the boats; it has a kiddies' play area, a large pond with ducks, and a snack bar which serves lovely coffee.
Best Way To Get Around:
Taxis can be a bit expensive, although there is a taxi rank opposite the hotel which seemed to be cheaper than the one that the hotel uses. The taxi driver that picked us up from the airport wanted to be paid up front for the return trip. There are lots of trips available, and we did a minibus trip with a short levada walk. Levada walks can be dangerous, so you should go with a guide.