I live in the city, so I know how hard it can be to find space to plant a decent garden. If you are just starting out, do not allow yourself to become overwhelmed by what you can't grow. Focus on what you do have room for, and make a start. As things get rolling, you will become more creative and may find more room than you thought that you had.
Grass is not a necessity. When we live in a town or city, we may feel the pressure to maintain a gorgeous looking, grass covered yard. However you can in reality garden your whole lot with not a blade of grass in sight. There are some communities that have rules and mandates about gardening in your front areas, but again with creativity this can be overcome. It is likely that you are allowed to plant trees, so try a dwarf variety of your favorite fruit tree. It will take a couple of years, but a fruit tree is wonderful to have.
Try using a container. If you only have a balcony or small patio space, container gardening will be your best bet. One tomato plant can provide you with a bountiful supply for a few weeks in the summer. Herbs, peppers, cukes, and lettuce are other great container plants.
Use the space wisely. Whatever space you have available to till, use it wisely. Raised beds or lasagna beds are a great way to make sure that you can use your space efficiently. Layer organic materials so that there is lots for your plants to use. You can then plant them more closely together. These types of beds are easier to weed and maintain.