Large Language Models (LLMs) are poised to play an increasingly important role in our lives, providing assistance across a wide array of tasks. In the geospatial domain, LLMs have demonstrated the ability to answer generic questions, such as identifying a country's capital; nonetheless, their utility is hindered when it comes to answering fine-grained questions about specific places, such as grocery stores or restaurants, which constitute essential aspects of people's everyday lives. This is mainly because the places in our cities haven't been systematically fed into LLMs, so as to understand and memorize them. This study introduces a novel framework for fine-tuning a pre-trained model on city-specific data, to enable it to provide accurate recommendations, while minimizing hallucinations. We share our model, LAMP, and the data used to train it. We conduct experiments to analyze its ability to correctly retrieving spatial objects, and compare it to well-known open- and closed- source language models, such as GPT-4. Finally, we explore its emerging capabilities through a case study on day planning.