A praying mantis will usually try to get to the highest place so that it can find something to hang upside-down from. It might stay on the plant because it would have to crawl all the way down to get off of it, which is against its nature. But don't try to put it on a vine plant hanging over a wall or on a smaller plant where it's only a short trip to the wall, tabletop or floor; once it gets there, there's no telling where it will wander to.
Also, they might be very peaceful and stationary sometimes, especially when they're big. Think of a mantis in the wild: if it's in a place where it gets a lot of food, it will want to stay on that plant. But in my experience there are certain times when a mantis will have the sudden urge to wander, and I'll see it roving around the cage all day. That happens when it hasn't eaten in a while (maybe looking for an area that has more insects in it), and when it is looking for a place to lay its eggs. So be warned that its habits could change suddenly.
Also in my experience, males wander much more than females (probably because they are looking for a mate) and will fly off to other parts of the house if it gets a chance. Males are also more likely to try to move towards light the way moths and bees do. Even when I kept them in jars, they would often escape.
Cats or some dogs will try to eat your mantis if it isn't protected, so be careful if you take it anywhere that has a cat.
Otherwise, good luck!