Start with Karen Radner's Ancient Assyria: A Very Short Introduction and her free online course Organising an Empire: The Assyrian Way.
Other good popular introductions include The First Great Powers: Babylon and Assyria by Arthur Cotterell and The Age of Empires: Mesopotamia in the First Millennium BC by Francis Joannès. Most of The Might that was Assyria by H.W.F. Saggs is still an excellent read, but the historical overview is now rather dated. Also take a look at Art and Empire: Treasures from Assyria in the British Museum.
A Companion to Assyria is a comprehensive overview of Assyrian history and society of all time periods, but it is a pretty dry read.
Other useful books on the Assyrians:
Assyria to Iberia at the Dawn of the Classical Age, a Metropolitan Museum exhibition catalogue
I Am Ashurbanipal: King of the World, King of Assyria, a British Museum exhibition catalogue
The Campaigns of Sargon II, King of Assyria, 721–705 B.C. by Sarah Melville
Sargon II, King of Assyria by Josette Elayi
Sennacherib, King of Assyria by Josette Elayi
The major Assyrian capitals that have been excavated are Aššur, Khorsabad, Nineveh, and Nimrud. For information on Aššur, see Assyrian Origins: Discoveries at Ashur on the Tigris (free PDF). Nimrud: An Assyrian Imperial City Revealed by Joan and David Oates is the best available synopsis of the excavations at Nimrud. The recently published Nineveh, the Great City: Symbol of Beauty and Power provides a complete overview of Nineveh from the prehistoric to Parthian periods.
Additionally, there's chapters on Aššur and Nineveh in Mesopotamia: The Invention of the City by Gwendolyn Leick, and Royal Cities of the Biblical World has a pretty good chapter on Nineveh as well.