Pacific Coffee are mostly in tourist/expat/yuppie areas, as well as in large shopping malls. According to their website, they only have one store in Mongkok, on Prince Edward Road West; and one in Jordan - inside the Queen Elizabeth Hospital.
Of their 5 stores in TST, the northern most one is in the Miramar.
Starbucks have more stores in the area - including Nathan Hotel in Jordan, the Gala Center on Dundas Street, etc... But, no free computer to use, of course.