Software Fault Localization refers to the activity of finding code elements (e.g., statements) that are related to a software failure. The state-of-the-art fault localization techniques, however, produce coarse-grained results that can deter manual debugging or mislead automated repair tools. In this work, we focus specifically on the fine-grained identification of code elements (i.e., tokens) that must be changed to fix a buggy program: we refer to it as fix localization. This paper introduces a neural network architecture (named Beep) that builds on AST paths to predict the buggy code element as well as the change action that must be applied to repair a program. Leveraging massive data of bugs and patches within the CoCoNut dataset, we trained a model that was (1) effective in localizing the buggy tokens with the Mean First Rank significantly higher than a statistics based baseline and a machine learning-based baseline, and (2) effective in predicting the repair operators (with the associated buggy code elements) with a Recall@1= 30-45% and the Mean First Rank=7-12 (evaluated by CoCoNut, ManySStuBs4J, and Defects4J datasets). To showcase how fine-grained fix localization can help program repair, we employ it in two repair pipelines where we use either a code completion engine to predict the correct token or a set of heuristics to search for the suitable donor code. A key strength of accurate fix localization for program repair is that it reduces the chance of patch overfitting, a challenge in generate-and-validate automated program repair: both two repair pipelines achieve a correctness ratio of 100%, i.e., all generated patches are found to be correct. Moreover, accurate fix localization helps enhance the efficiency of program repair.