I only went to those two places in Summer.
It should be pretty easy to get a cabin at the Grand Canyon this time of year. Maswik and Kachina aren't anywhere near full yet. If you're flexible with times, you might even be able to get a cabin at Bright Angel Lodge since most dates are available. Then there are the pricier places like the El Tovar Hotel and Thunderbird Lodge, which do have plenty of availability, although some dates seem to be full. We stayed at Maswik because it could be reserved, but if it were available, the Bright Angel cabins would have been preferred for their history and location. Maswik was cheap and more than acceptable, but the location wasn't that close to the rim and the architecture was rather unremarkable. Here's one of the Bright Angel cabins:
If you're going to Zion, I guess you could stay at Zion Lodge, but this time of year you can drive yourself and Springdale is quite convenient. I stayed at the Quality Inn at Zion Park. It thought it was a good bargain, the rooms were decent sized and well maintained (it looked to be pretty new though), and the service was friendly. They had a free continental breakfast, and the owner was proudly making fresh waffles. Of course when I went it was 100 degrees outside and I stayed in my air-conditioned room during the mid-day heat.