Chamonix is great for advanced off piste. There are some really classic routes, although with the glacier dropping some are getting quite dangerous, like the Pas de Chèvre.
My advice would be to use a guide if you want to get the most out of Cham. Just join the ‘guide day’ group which you can book at the Guides Office. It’s quite cheap at around 85 euros and you just ski with whoever else has pitched up. You meet some interesting people and enjoy a guided day for a fraction of the price of hiring your own guide. Often the guides prefer to go through to Courmayeur and there are great off-piste routes there too. The food is better there too!