Funchal Airport (IATA: FNC) is in nearby Santa Cruz, sometimes known as Madeira international/Santa Catarina/Funchal. Once famous for its hair-raisingly short runway ending at a cliff over the Atlantic Ocean, the airport has been expanded to handle all sizes of aircraft. There are several daily flights from most major cities in Portugal (Lisbon,Porto). Flight time from Lisbon is 1 1/2 hours. Also, there are good connections from London (mostly Gatwick)(LGW), with TAP/ Air Portugal(TP) and British Airways(BA); its flying time is estimated at 3 1/2 hours.
The city centre is small enough to explore on foot. Orange city buses can take you around and up to Monte (lines 20, 21). Buy a giro card from the office for 2,20€, it is already preloaded with two journeys and can be topped up with additional journeys for 1,50€ a piece. Most city buses start from the waterfront area.
Madeira Botanical Gardens (Jardins Botânicos da Madeira), Caminho Meio Quinta do Bom Sucesso (about 3km from downtown). The more than 2000 plants of these hillside gardens make this one of the major attractions of the whole island.
Monte Palace Hotel Gardens. The gardens of this defunct hotel include a Chinese garden, artwork, a small lake, and a variety of flora and fauna.
Santa Clara Convent (Convento da Santa Clara), Calçada de Santa Clara 15. Dating from the end of the 15th century, this convent, now a national monument, was founded by João Gonçalves da Câmara. The azulejo tiles are especially notable.
São Lourenço Palace (Palácio de São Lourenço), Avenida Zarco. Half fortress and half palace, this construction is a good example of mannerist architecture. Highlights include the Noble Salon (Salão Nobre), the Green Room (Sala Verde), the Audience Hall (Sala de Audiências), and the gardens.
Sé Cathedral. The central point in Funchal, and its most-visited monument. Commissioned by the king Dom Manuel I through Portuguese explorer Gil Eanes, the cathedral was built between 1493 and 1517. The ceiling is made from local wood.
Visit the fair/market; old port; jardim; casino. Enjoy Birdwatching.
Flowers,fruit (check with the airline/ship if they can be brought abroad).
The island is world-famous for its wines. Several stores offer varying selections. Consult Wikipedia  and other sites for details.
Funchal has an abundance of good, if not necessarily cheap, eating places. Most places serve traditional Madeiran and Portuguese food, which is well-prepared and well-tasting, but not terribly exciting. One of the most typical dishes and served almost everywhere, is espada com banana, scabbard fish with banana. It is usually served with fresh salad and potatoes. A bit more expensive, bacalhau (dried, salted codfish) is served in many restaurants. One of the more common, and best, varieties is "bacalhau com natas", codfish in cream sauce.
Bar Beer Garden, Estrada Monumental, Arieiro. Recommended dish is Picado (beef steak served with chips). The normal size (10 euros) should be enough for 2 persons. The bigger size (13 euros) could serve 3 - 4 persons.
Golden Gate Grand Café, Avenida Arriaga 21. Very centrally located, straight across the street from Palácio de São Lourenço. Its coffee, pastries, food and service is excellent and the café, opened in 1814, has a nice atmosphere with a good mix of local customers and tourists.
O Castelo Dos Hamburguers, Rua da Carreira, 306, Tel: + 351 291 756616. This place sells only 3 types of prego-style hamburgers: normal, special and super. Also try their smoothies. 
Inquire at the hotel for English, Germanic, Scandinavian pubs/bars.
Doca do Cavacas, Estrada Monumental, Ponta de Cruz, Tel: + 351 291 762057. Fish restaurant.
Japanese Restaurant, 2nd floor, Monumental Lido Shopping, Lido. Buffet lunch for 10 euros.
Xôpana Restaurant, Choupana Hills Resort and Spa, Tel: (+351) 291 20 6020. Award winning restaurant at the Choupana Hills Resort, with a magnificent view over Funchal and world-class food and wine.
Les Faunes, Estrada Monumental 139, In Reid's Palace Hotel, Tel: 291/71-71-71. Top quality French restaurant.
Not the party capital of the world. Most of bars are very quiet. No decent Irish bars. Some think the best bar is Glorias Latino.
Bar Amazónia, Rua de São Filipe 19, ☎ (351) 291 228 164. A pleasant little bar.
Café do Teatro, Avenida Arriaga Ed. Teatro Municipal Baltazar Dias, ☎ (351) 291 226 371.
Chameleon Disco-Bar, Rua Imperatriz D. Amelia Nº119 (in front of the Carlton), ☎ (351) 291 228 038. Café and bar with a tropical atmosphere. Karaoke on Mondays and Tuesdays, live music on Thursdays, and ladies' night on Sunday.
FX Bar, Largo das Fontes 39, ☎ (351) 965-077-875.
Madeira Casino, ☎ (351) 291 209 180, . The only casino on the island. Designed by Oscar Niemeyer.
Vespas, Avenida Sá Carneiro 60. Dance club very popular with young people.
During low season (winter) prices may drop significantly, e.g., from 50€ to 35€. Time around Christmas is high-season.
Apartamentos Sao Paulo and Apartamentos Alegria. Owned by the Mendonza family. Has 2 apartment blocks. Located in the Old Town, close to the English Church & Rua da Carreira. Cheaper rates for weekly stays.
Residencial Melba (Melba Pension), Azinhaga da Casa Branca 8. Lies in Western Funchal. 12 rooms.
Pestana Hotels & Resorts - Funchal: Pestana Miramar, Pestana Village, Pestana Palms, Pestana Bay, Pestana Gardens 
Quinta Perestrello Heritage House, Rua Drº Pita nº 3, . A small hotel, One adult 33€ per night and breakfast (special offer low season), 37 double rooms, located near Reid's Palace. 24 hour reception.
Hotel Monte Carlo, Calçada da Saude Nr. 10. Beautiful, old hotel with a great view over the city of Funchal. Directly near the Convent St. Clara. Reasonable priced and not directly in a desiganted tourist district. Lots of good and affordable restaurants nearby.
Pestana Hotels & Resorts - Funchal: Pestana Carlton Madeira, Pestana Casino Park, Pestana Grand 
Choupana Hills Resort, Travessa do Largo da Choupana, (351) 291 20 60 20, . One of the top hotels in Madeira just outside Funchal.
The Cliff Bay ((Porto Bay Hotels & Resorts)), Estrada Monumental, 147, ☎ (+351) 291 707 700 (firstname.lastname@example.org, fax: +351 291 762 525), . direct access to the sea, stunning views over the Atlantic and Funchal´s bay, one michelin star restaurant.