The Kitāb al-Așnām or Book of Idols has been translated into English and is available for free online; this was a c. 800 AD book on pre-Islamic religions in the Arabian Peninsula - granted, written a couple hundred years after the rise of Islam and from a distinctly pro-Islam perspective, so plenty of grains of salt to be taken, but it gives an idea from an Islamic perspective of pre-Islamic religion and mythology at the period.

As another poster (u/AncientHistory) pointed out, al-Kalbī's Kitāb al-Asnām is an important work. He also pointed out some of the problems in using it as a primary source, but I would just like to add that the book was not that well-received even by other Muslim scholars at the time. I'll have to look up the exact citations, however.

General overview

• Hoyland, R. (2011) Arabia and the Arabs: From the Bronze Age to the Coming of Islam. Although it's not a revolutionary book, Hoyland still gives an indispensable overview of what we actually know from pre-Islamic Arabia. Hoyland goes from region to region, so you might have to check each chapter individually to see what he says about religion and beliefs. There is actually a chapter entitled "Religion", so it would make sense to look there!

Syria

• Teixidor, J. (1979) The Pantheon of Palmyra. As you can see by the age, it's already a bit dated, but still a fascinating read if you want to know more about the religious environment on the edges of Arabia before Islam.
• Fischer, G. (2011) Between Empires: Arabs, Romans, and Sasanians in Late Antiquity. Basically Fischer talks about everything during the Late Classical period, and bases himself mostly on Roman sources (he himself indicates he's not an Arabist by training).

The Peninsula

• Crone's "The Religion of the Qur'anic Pagans" and "How Did The Qur'anic Pagans Make a Living" are two articles which talk, as you can see, about how the mušrikūn of the Qur'an are described. These articles were recently integrated in a volume entitled The Qur'ānic Pagans and Related Matters
• For Southwest Arabia you could try looking for articles written by Norbert Nebes and Peter Stein, although they more directly treat history and linguistics specifically. There's a lot more available material in French, if you can access that, mostly by Christian Robin, who has written really interesting stuff on the conversion of Yemen to Judaism and its relationship to the Israelites.

I think that's pretty much most I have in my head right now, and I think this will get you a long way. If you really run out of stuff you can just respond to this post or drop me a pm.

The Nabataeans were a people that lived in northwest Arabia and Syria in the classical era (best known for building Petra) and are generally associated with the ancestors of the Arabs. We know a fair a bit about their religious practices from archaeology and inscriptions, see:

• Healey, John F. 2001. The Religion of the Nabataeans: A Conspectus
• Bartlett, John R. 2007. Nabataean Religion. In K. D. Politis (ed.) The World of the Nabataeans, vol. 2.
• Alpass, P. 2013. The Religious Life of Nabataea

The Wikipedia article is also not that bad as a starting point.