Most of your training should take place in the class, as it is a safe environment to be, i.e. not knocking over coffee cups or tv's
Things to do at home would be stretching, Find a area you can sit down in with nothing around, and practise some stretching techniques. If you stretch regularly then you will be surprised how much this can help in your training.
Patterns is a great thing to practise in the home, and you don't need a lot of room for this, standing on the spot and running through the pattern is a great way of getting it in your head, ask your instructor for more information on doing this.