High-accuracy and low-latency indoor place prediction for mobile users can enable a wide range of applications for domains such as assisted living and smart homes. Previous studies used localization techniques that are difficult to deploy, may negatively impact user privacy, and are not suitable for personalized place prediction. To solve these challenges, we propose GoPlaces, a phone app that fuses inertial sensor data with distances estimated by the WiFi Round Trip Time (WiFi-RTT) protocol to predict the indoor places visited by a user. GoPlaces does not require help from servers or localization infrastructure, except for one cheap off-the-shelf WiFi access point that supports ranging with RTT. GoPlaces enables personalized place naming and prediction, and it protects users' location privacy. GoPlaces uses an attention-based BiLSTM model to detect user's current trajectory, which is then used together with historical information stored in a prediction tree to infer user's future places. We implemented GoPlaces in Android and evaluated it in several indoor spaces. The experimental results demonstrate prediction accuracy as high as 86%. Furthermore, they show GoPlaces is feasible in real life because it has low latency and low resource consumption on phones.