Taking your cat for a walk is not like taking a dog for a walk. Often the purpose of taking dogs for a walk is for them to relieve themselves. An indoor cat doesn't need to do that on the walk.
Walking your indoor cat outdoors gives your cat stimulation that can't be found indoors. There are new things to see, hear, smell, feel, and even taste (though you'll need to be careful about what might be tasted). A walk isn't simply a walk but an exploration of a new world.
This new world can be a little overwhelming at first for an indoor cat that hasn't spent any time outdoors. As such, it's a good idea at first to stay close to home and start off slow so your cat isn't overwhelmed. Once your cat becomes more comfortable you can build up to more stimulating adventures.
Here are some ideas for where to walk your cat.
You might not find your back yard very interesting but a cat who never goes outside might find it fascinating with all the new smells, the feel of the grass, the buzzing of insects, etc. It's a great starting place for your cat to get comfortable with being outdoors. Remember, you have no destination. Just let your cat explore at its own pace. You might lead your cat to certain places that will catch its attention.
If you live in an apartment or condo complex then you'll have the common grounds of the complex to explore. You may have an open field with a pond or you may only have smaller landscaped areas. Stick with the quiet areas at first until your cat becomes more comfortable being outside on leash.
Gardens are full of all sorts of scents and spaces for your cat to explore. There may be gardens on your property or on the common grounds of the complex you live at. If you live in a shared building you may even have courtyard or rooftop gardens to explore. You can eventually take your cat to neighborhood and community gardens once you cat is ready for more.
As your cat becomes more comfortable outdoors and on leash you can venture to more wide open areas to explore that can be found in neighborhood and public parks. Know your cat's comfort level and avoid people, animals, and activities that take your cat beyond that comfort level. Consider whether it's OK to walk your cat to the park or whether you need to transport your cat to the park before starting your walk.
School campuses often have a lot of open fields, landscaping, playgrounds, and pathways to explore. This is especially true of college campuses. There may also be some buisiness company or public building campuses in your area to explore as well. Just make sure your visit doesn't violate some rules about animals or trespassing.
Taking a walk through nature takes your cat back to its roots. Some of these trails may meander around water features full of wildlife. Other trails may be woods-like where your cat can walk on different surfaces from dirt to leaves to rocks to logs. All-in-all it can be a different experience from the landscaped areas where people live.
Once your cat has spent time exploring this new outdoor world your cat may enjoy just walking and not take as much time exploring. Walking trails offer a space to do that away from the roads and a lot of noise. Just be prepared for when you'll be crossing paths with others walking the trails, especially those who might be walking their pets.
What all the places above have in common is that they are away from noise, traffic, and crowds. You want your cat to feel safe and not overstimulated. Over time your cat may take to walking almost anywhere. Start off slow and see where it goes.
There are also alternatives to walking your cat on leash where your cat can get used to and enjoy the outdoors without actually having to walk. These alternatives can be combined with walking on leash. They are also good ways to transport your cat to where the walk on leash begins.
Alternatives to walking your cat on leash: carriers and strollers
You may want to scout out public areas first before taking your cat so you can not only see if it's a place your cat would enjoy but also determine the rules about walking pets in those locations (i.e., whether pets are allowed, whether there are designated areas, etc.).
Remember that you don't have to start your walk right from your home. You can transport your cat to the walk destination before beginning your cat's walk. This offers many more options than just what's immediately around your house. Though you'll probably want to make sure your cat won't try to escape before venturing too far from home.