Albany is the oldest European settlement in Western Australia and was a major whaling station, and coal shipping port. There is also a large amount of Aboriginal evidence from earlier times in Albany.
There are fantastic views over the town of Albany, and the fantastic coastal scenery from the top of both Mt Clarence and Mt Melville. Mt Clarence is to the east of the town, and can be reached along Apex Drive. Mt Melville is to the west of the city and can be reaches from Serpentine Road. For other great views, and an interesting place to visit head to the Princess Royal Fortress on Mt Adelaide.
There are a number of historic buildings around Albany, including the magnificent Victorian buildings along Stirling Terrace. More buildings with fine architecture include the Courthouse, St John's Anglican Church and the Town Hall. You can also visit the interesting Albany Residence Museum, which is next door to the Amity which arrived with Albany's settlers in 1826. If you want to see all of the main sights, then you should follow the Albany walking tour which is very enjoyable. To the north of the town, are the Albany Botanic Gardens, as well as Dog Rock which is a rock in the shape of a dogs head (surprisingly enough).
Around Albany there are a number of good beaches and pretty coastline. Frenchman Bay, Middleton Beach and Two People's Bay offer good swimming beaches, while Jimmy Newhill's Harbour and Salmon Holes offer great surfing beaches. (If you do go surfing here be careful, as although the waves are good they can be very dangerous).
From Albany one great tour which you should go on is whale watching, where you get to see the Southern Right Whales during their migration between July and September. There are various boat charters which offer this tour as well as tours to the nearby Fitzgerald River National Park and West Cape Howe National Park, which offers fantastic bushwalking and rock climbing. Another nearby National Park is the Torndirrup National Park which features a number of Blowholes, and the wonderful Gap and Natural Bridge which are the highlights of the park. You can also visit the Waychinicup National Park which hosts a number of rock formations.
There is a selection of accommodation around Albany, including campsites, hostels and guesthouses. Much of the accommodation is along streets off of York Street, with restaurants along Frederick Street, Stirling Terrace and York Street. If you don't have your own transport you can get around Albany by bus.