We present CoNVOI, a novel method for autonomous robot navigation in real-world indoor and outdoor environments using Vision Language Models (VLMs). We employ VLMs in two ways: first, we leverage their zeroshot image classification capability to identify the context or scenario (e.g., indoor corridor, outdoor terrain, crosswalk, etc) of the robot's surroundings, and formulate context-based navigation behaviors as simple text prompts (e.g. "stay on the pavement"). Second, we utilize their state-of-the-art semantic understanding and logical reasoning capabilities to compute a suitable trajectory given the identified context. To this end, we propose a novel multi-modal visual marking approach to annotate the obstacle-free regions in the RGB image used as input to the VLM with numbers, by correlating it with a local occupancy map of the environment. The marked numbers ground image locations in the real-world, direct the VLM's attention solely to navigable locations, and elucidate the spatial relationships between them and terrains depicted in the image to the VLM. Next, we query the VLM to select numbers on the marked image that satisfy the context-based behavior text prompt, and construct a reference path using the selected numbers. Finally, we propose a method to extrapolate the reference trajectory when the robot's environmental context has not changed to prevent unnecessary VLM queries. We use the reference trajectory to guide a motion planner, and demonstrate that it leads to human-like behaviors (e.g. not cutting through a group of people, using crosswalks, etc.) in various real-world indoor and outdoor scenarios. We perform several ablations and navigation comparisons and demonstrate that CoNVOI's trajectories are most similar to human teleoperated ground truth in terms of Fréchet distance (9.7-58.2% closer), lowest path errors (up to 88.13% lower), and up to 86.09% lower % of unacceptable paths.