Natural disasters can have devastating and long-lasting effects on a community's emotional well-being. These effects may be distributed unequally, affecting some communities more profoundly and possibly over longer time periods than others. Here, we analyze the effects of four major US hurricanes, namely, Irma, Harvey, Florence, and Dorian on the emotional well-being of the affected communities and regions. We show that a community's emotional response to a hurricane event can be measured from the content of social media that its population posted before, during, and after the hurricane. For each hurricane making landfall in the US, we observe a significant decrease in sentiment in the affected areas before and during the hurricane followed by a rapid return to pre-hurricane baseline, often within 1-2 weeks. However, some communities exhibit markedly different rates of decline and return to previous equilibrium levels. This points towards the possibility of measuring the emotional resilience of communities from the dynamics of their online emotional response.