This paper presents a novel Grouping Harmony Search (GHS) algorithm for the Citywide Ubiquitous WiFi Network Design problem (WIFIDP). The WIFIDP is a NP-hard problem where private customers owning wireless access points connected to Internet share bandwidth with third parties. Aspects such as allocated budget and router capacities (coverage radius, capacity, price, etc) are taken into account in order to obtain the optimal network deployment (in terms of cost-effectiveness) when applying the GHS algorithm. The approach to tackle the aforementioned WIFIDP problem consists of a hybrid Grouping Harmony Search (GHS) algorithm with a local search method and a technique for repairing unfeasible solutions. Furthermore, the presented GHS algorithm is differential, since each proposed harmony is produced (improvised) based on the same harmony in the previous iteration. This differential scheme employs the grouping concept based on the connectivity between nomadic users and routers, which increases significantly its searching capability. Preliminary Monte Carlo simulations show that this proposed technique statistically outperforms genetically-inspired algorithms previously presented for the WIFIDP, with an emphasis in scenarios with stringent capacity and budget constraints. This first approach paves the way for future research aimed at applying the proposed algorithm to real scenarios.