Star, it depends on how much hiking you like to do -- yes, there could be seven days' worth of hiking at Zion, especially if you go into the back country on long day hikes. But personally, if this is your first time to both Bryce and Zion, I would split it up. Bryce is a very long day trip from Zion, and the camping and hiking there are really great.
So I would spend three days in Zion, a travel day, and three days in Bryce. Zion will be quite warm. Bryce will be very cool. If possible, bring bikes to Zion -- the ride from the bottom to the top of the canyon is very easy, and the glide downhill is fun. Plus there are no cars -- I think that the shuttle buses will be running at that time.
If you are adventurous, try the Narrows at Zion -- you may want to rent special wading gear in town.
Let us know if you want some specific recommendations for hikes in both places. How many miles a day do you usually do, and how much elevation gain can you handle? (I max out at about ten miles round trip, with about 2800 feet of climbing, depending on the terrain, but hikers in really good shape can handle a lot more than that.)
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