Iguana's need & Love branch's to climb on, I always make sure they are a little wider than the Iguana. They love to be up high =~)
They also like to have plants,fake or real in the tank / cage as well , gives them something to look at. I switch plants about once a month. (how boring would it be to look at the same thing all the time?)
In one of my cages I have large rocks - real ones not the fake stuff you buy from pet stores, I have found out they love to use them as a pillow. Something else is a big tub for them to soak in, and use the bathroom in. Iguana's do like to swim, soak and play in the water.
Its hard to say but I have learned over the years the more they have to climb on & look at the happier they are, so all of my cages are double decker's. top part being all branch's, rocks, & food area bottom part being water , more food area and more rocks both area's have plants both live and fake. They all get to spend a few hours a day out of their cages as well.
They love to sit in the window and watch whats going on outside. Each Iguana is different so what one may like another may not. One of our rescues used to only sleep with a pillow case he loved that thing & would not sleep without it.
I never have really seen any of mine play with a 'toy' so that I am not sure of.
ha lol I totally forgot! They do need heat lamps , day lamps and UVB lights are a must!