We present a model to predict spatial hotspots, defined as the regions in a future time period that have the highest proportion of events of interest. We assume the conditional intensity of the events of interest can be influenced by geospatial and temporal predictors as well as nearby events from other point processes, a common assumption in crime and conflict processes. Likewise, our model explicitly incorporates the characteristics of the spatial environment, temporal trends, and estimates the influence of past events. As a variation on traditional self-exciting (Hawkes) point process models, we directly model the probability that a location will be a member of the hotspot in a future time period. We use a penalized logistic regression model that allows the spatial covariates and each event type to have a different effect (including inhibition) on the probability. The duration of an event's influence is modeled by a mixture of decay functions resulting in a flexible and interpretable dependence structure.