I'd also recommend staying in the park at Trailer Village. The free shuttle stops right there and you can even walk to the Rim. It's the easiest way to visit the Canyon and you'll want to be there at least two nights to really enjoy it. It's best early morning at late afternoon/evening when the majority of folks thin out.
Taking the train from Williams is a long day and you're only at the Canyon a couple hours before having to return. It's definitely not enough time if you're making the effort to really 'see' the Canyon. There are many ranger programs and an easy hike along the Rim getting off and on the shuttle bus whenever you want. I'd also recommend that you hike below the Rim on the Bright Angel Trail if only for 1/8 mile or so. It will give you an altogether different perspective of the Canyon. Also plan to be at the Rim at sunset. It's always a great show!