The oldest part of Amsterdam has a lot of interesting buildings, most notably Oude Kirk and the splendour of the Royal Palace. The red light district is in this area, between Centraal Station, Nieuwmarket and the Dam, as well as the Jewish Quarter which is centred around Waterlooplein.
The western part of the canal ring that surrounds the Old Centre is an excellent place to find cheap Amsterdam hotels and quieter restaurants and eateries. The streets tend to be quiet and are a great wander around for a good look at the canal houses. One of Amsterdam's most famous attractions, Anne Frank House is situated here.
The canals of the Central Ring are generally quite busy and there are lots of little museums and shops to find, such as the Museum van Loon where you can look round a lavish aristocratic canal house and the Museum of Bags and Purses. The flower market near Rembrandtplein is a great place to see the bright tulips without travelling to the countryside.
The eastern section of the canal ring is a great place to find a bit of open space close to the old centre. There are botanical gardens at the Wertheim Park and at Artis you can find a zoo boasting plenty of listed buildings as well as lots of animals and an aquarium.
Just outside the canal ring and next to Vondelpark is the Museum Quarter, with the majority of the attractions centred around the Museumplein, boasting the Rijksmuseum, Van Gogh Museum, and the Stedelijk Museum of Modern Art. The surrounding area is known for its culture and fashion so there are plenty of great shops and quirky places to visit.
The city centre offers more than enough for your first Amsterdam holiday (and maybe the second too!) but other areas to visit include Jordaan, west of the western ring, known for its charming character and proliferation of galleries, and De Pjip to the east of the Museum Quarter where a melting pot of nationalities means that a diverse shopping experience and a wide selection of restaurants is on offer.