CR,
I believe you are correct, as far as the Stanley Cyber Cafe being the nearest Internet Cafe to Hotel de la Montagne with more than 1 machine. The Stanley Cyber Cafe has about 20.
The only other decent Internet Cafe remotely in that area is the Battle Net across the street from the Hotel du Fort on du Fort, but that is a substantial walk of at least 15 minutes from the HDLM.
The Battle Net is open 24/7 but that Stanley Cyber Cafe is only open 9-5 Monday Friday, 10-5 Saturdays and closed Sundays. So if you need to access the Internet very late at night or early in the morning, you will need to go to the Battle Net on du Fort.