What do we know about the location of Islamic schools in pre-colonial Africa?

The short answer is: where there was even a small Muslim population, there were usually schools for children at the elementary level, even in villages. Overall, we are thus talking about numbers which dwarf the number of Christian missions.

Without a basic religious education, Muslims cannot perform the duties required of them. Some of these schools were very small (less than 10 children); it is thus highly unlikely that maps or comprehensive data exist for large areas of pre-colonial Africa (never mind all of sub-Saharan Africa), but there is data for some regions in the early colonial period (links below).

In West Africa,

The mobility of...Walking Qurʾan made Islam a familiar feature of West African life. Itinerant scholars, teachers, and preachers were known even in non- Muslim or religiously mixed areas....Large clerical families produced dozens of huffāẓ, many of whom would then go out to remote villages and open Qurʾan schools. The natural and social reproduction of these clerical lineages scattered scholars throughout the region, and by the eighteenth century, few villages lacked a Qurʾan school teacher.

Source: Rudolph T. Ware III, 'The Walking Qur'an: Islamic Education, Embodied Knowledge, and History in West Africa' (2014) (my emphasis)

The above does need qualifying a little in that the populations of the coastal regions of pre-colonial West Africa to the south of Senegal were overwhelmingly animist, and large areas of dense forest had very low populations. It is thus unlikely that there would have been many villages with schools in much of the forest zone.

"A Qurʾan school in Dakar, Senegal, from an early twentieth- century French postcard". Source: Ware, p2

In Zanzibar in East Africa, the number of Qur'an schools for children (known locally as vyou) "increased manyfold" under Omani rule. Higher education, though, was much more restricted and generally only available to local elites. Similary, in the Sudan,

By the early nineteenth century a rough hierarchy of religious "schools" existed in the region, with most villages having a place (usually a mosque or a teacher's home) where children learned the Arabic alphabet and how to read and write passages from the Koran.

(my emphasis)

Looking at contemporary sources, the Scottish explorer Mungo Park (1771 - 1806), in Travels in the Interior of Africa commented on the ready availability of schools in towns. Also, during the early colonial period, Paul Marty (1882 - 1938) wrote a series of volumes on Islam in what was then French West Africa, including some fairly detailed data on the numbers of schools. See, for example:

• Études sur l'Islam au Sénégal
• Les écoles maraboutiques du Sénégal
• Études sur l'Islam en Côte d'Ivoire
• L'Islam et les tribus dans la colonie du Niger
• Études sur l'Islam et les tribus du Soudan (modern-day Mali)

A word of caution: Paul Marty was a military officer and colonial official, not a scholar, and he often had a poor understanding of what he was writing about. Also, some of his views are highly offensive and demeaning (in my estimation, more so than most other European writers of the period). Nonetheless, you may find his data and maps useful. For example, there's this table showing the number of schools and pupils in northern Ivory Coast in 1919:

Source: Études sur l'Islam en Côte d'Ivoire.

The widespread existance of schools for Muslims, known variously as kuttab, maktab, maktaba, Qurʾan schools, ecoles coraniques, ecoles maraboutiques etc., makes it unlikely that a map plotting them exists for all of sub-Saharan Africa; there were simply too many in predominantly Muslim regions. Also, mosques often had schools attached to them.

One way of getting a geographical handle on elementary schools is to look at data for the percentage of Muslims in different regions of sub-Saharan Africa. The maps below give an idea of the reach of Islam before the colonial era and for 1900. However, we probably cannot assume an exact correlation between Muslim population and number of Qur'an schools.

Pre-Colonial

Map source: Geography

1900 / Early Colonial

Map source: Stelios Michalopoulos, Alireza Naghavi & Giovanni Prarolo, 'Trade and Geography in the Origins and Spread of Islam' (2012)

The extent of Christian missionary activity was partly determined by the presence or otherwise of Islam, but it's a complex picture. The coastal regions of West Africa were early targets as settlements were easily reached from the sea and Islam, by and large, was not present.

Nonetheless, attempts were made to set up missions further inland with varying degrees of success. The Pères Blancs (White Fathers), founded in 1868 in Algeria, had a mission in Timbuktu until 1906 but, generally, attempts at 'invading' regions which had long been Muslim failed. In heavily Muslim northern Nigeria,

There were various attempts to establish mission stations in Northern Nigeria between 1855 and 1900, which were met with varying degrees of success

Ultimately, it was the British system of indirect rule which ensured an end to the missions

Indirect rule meant that the protectorate of Northern Nigeria would be administered by the Emirs of the Islamic Sokoto Caliphate in the Northwest, and the Islamic Borno Emirate in the Northeast...

...missionary activity in Northern Nigeria was significantly restricted by the policy prohibiting missionary activity from most parts of Northern Nigeria under the control of the Emirs

Further south, in Bugunda, it was a different. Although Islam got to the region first (mid 1840s), this did not stop Christian missionaries arriving in the 1870s & 1880s and halting Muslim penetration. The rivalry between Protestants, Catholics and Muslims ended up with Protestants coming out on top, favoured as they were by the British colonial officials. However, Islam did not disappear but Muslims were disadvantaged education-wise.

In what is now Tanzania, the situation was different again; despite German and the British colonization, Quaran schools actually increased in number due to improved communications but, ultimately, those educated in Christian missions came to hold an advantage in jobs and prospects. Details can be found in Philemon Andrew K. Mushi's History and Development of Education in Tanzania