I can recommend two books by Barry Cunliffe, a prominent archaeologist and writer that has churned out some amazing books. Steppe, Desert, and Ocean: the Birth of Eurasia takes a broad approach to Asia, and surround regions like East Asia and Europe, but contextualizes the steppes and central asia quite well. It details quite a long time range as well, and may be a good place to start. The Scythians: Nomad Warriors of the Steppe is a detailed treatment (with lots of illustrations) of the Scythians.

A concise overview of the Huns can be found in The Huns, a recent entry in Routledge's "Peoples of the Ancient World".

A History of Inner Asia is a succinct introduction that looks at Inner Asia as a whole from the emergence of Islam to the present. It covers the Turks and the Mongols. The Turks in World History looks at the difference societies of the Turks, from medieval times to the present.

The Mongols is a good introduction to said people. The Mongols and the West is great for a treatment relative to Europe, while The Mongols and the Islamic World: From Conquest to Conversion is great for the Middle East (though this one appears to be pretty expensive at the moment).

If you want to go back further with the steppes (and thus into even more archaeology-heavy and murkier histories), then try the popular The Horse, the Wheel, and Language, which goes into the regions Bronze Age, Proto-Indo-European origins and its involvement with horse domestication.

And Christoph Baumer has been releasing his 4-part history of Central Asia. These are huge books, really heavy with lots of high definition photos, and is a good overall look into the region as a whole. Cambridge has a couple books on Central Asia as well, though the earlier book (Early Inner Asia) is getting to be a little old by now.