Given a set of points in two dimensional space, a minimum radius, a minimum log likelihood ratio and a significance threshold, Geographically Robust Hotspot Detection (GRHD) finds hotspot areas where the concentration of points inside is significantly high. The GRHD problem is societally important for many applications including environmental criminology, epidemiology, etc. GRHD is computationally challenging due to the difficulty of enumerating all possible candidate hotspots and the lack of monotonicity property for the interest measure, namely the log likelihood ratio test. Related work may miss hotspots when hotspots are divided by geographic barriers (the road network, rivers etc.) or when hotspot centers are close to parks, lakes, mountains, etc. To address these limitations, a novel approach is proposed based on two ideas: cubic grid circle enumeration and a grid log likelihood ratio upper bound. A case study on real crime data shows that the proposed approach finds hotspots which cannot be discovered by the related work. Experimental results show that the proposed algorithm yields substantial computational savings compared to the related work.