Most of Melaka's sights are clustered around the base of St Paul's Hill on the southeast side of the river. Between the hill and the river is the old Dutch town square. From the square, you can climb the hill up to St Paul's Church at the top. Descending the other side of the hill will bring you to the remains of the A'Famosa fortifications built by the Portuguese. Around the ruins of the fort are several museums of interest, including the Proclamation of Independence Memorial and the Cultural Museum, housed in a reconstruction of the Sultan's Palace.
Back on the river front, not far from the town square, is the Maritime Museum. Crossing over the river will take you into Melaka's Chinatown, where you'll find rows of beautifully decorated shophouses as well as Chinese temples, Hindu temples and Mosques.
Speaking of the river, up-stream from the Chinatown area is Melaka's only Malay kampung to retain it's original traditional style. It's something of a 'living museum' in that it continues to function as a home for locals. The name comes from Frederic Joseph Morten, a British Land Commissioner who is believed to have had a hand in opening the village. The house belonging to the village's founder, Villa Sentosa, is open to the public, with displays of traditional clothes and furniture.
Somewhat further afield is China Hill, now the largest Chinese cemetery outside of China. About one kilometer due north of the old Dutch Town Square is St Peter's Church, the oldest Catholic Church in Malaysia where services are still held. Three kilometers down the coast is the Portuguese Square.