My guess is that the SII can easily drive a lot of headphones out there. But to recommend one, knowing some information would help - such as, budget and the kind of sound signature you like (e.g. warm, neutral, analytical, bassy, etc.)
If you're new to headphones and are not sure what kind of sound you like, a good starter pair would be the Sennheiser HD600 or HD650 (which is the same as the cheaper Massdrop HD6XX.) Those are widely popular, well regarded, and have a sound signature agreeable to many ears. They'll make good references as you journey down the headphone hobby.
Good luck.