I live in Phoenix and traveled to Page/Lake Powell to work a few days each month for 3 years. Antelope Canyon and Horseshoe Bend are definitely worth doing on your way to the national parks. I used to stop by Horseshoe Bend on my way home from work in the morning sometimes, just to get some fresh air and enjoy the view and shake off work stress. Horseshoe Bend is about a 10-minute walk from the car to a jaw-dropping view.
A nice scenic drive, if you have a national parks annual pass anyway, is to go into the Glen Canyon National Recreational Area (Google Lake Powell Resort and go in that entrance) and just drive around. It only takes about 10-15 minutes, plus whatever time you want to stop for photos. The road goes along the lake, and there are excellent views.
Also consider getting a permit ($10 or so) for Water Holes Canyon, which is a relatively short hike just off route 89, just south of Horseshoe Bend. (Google for where to get the permit... I've forgotten the specific locations.) It's similar to Antelope Canyon, but you don't need to pay a guide. When I went, I was the only one there until I ran into another couple at the very end.
If you happen to have enough time, kayaking the lower part of Antelope Canyon is a gorgeous way to spend an afternoon. Kayak Powell is a kayak rental outfit in Page. No need for a roof rack -- they'll hook you up with straps and pool noodles to carry the kayak(s). (Another nice kayak trip for another time, with people who camp, is to go from Lee's Ferry upriver (with a backhaul or on your own if you're a very strong kayaker) to the dam, then back down. You go through Horseshoe Bend, and there are really nice sandy campsites along the way. Stars at night like you wouldn't believe!)
I'm usually okay with heights, but I was absolutely terrified by Angel's Landing. I did it, but I will never do it again. Shockingly horrible. Beautiful views, though. If you're not bothered by the height and the steep drop-off inches from your feet, it's worth doing. (I may be a bit biased by the fact that on my first trip to Zion, there were body recovery crews looking for someone who had fallen off Angel's Landing.)
The Narrows hike is definitely a must-do. I'd take a couple of hiking poles or even just sticks to give yourself "four wheel drive" to help minimize slipping and falling into the river. (My then-boyfriend laughed at me for this and actually fell into the river while laughing. He now does hikes like that with hiking poles.) It's not very deep in most places, but it can be cold in May!
If you can get permits (see the national park website and Google for stunning photos) for the Subway, that's another must-do hike. It's similar to the Narrows in the sense that you hike up a very shallow (though not narrow until the subway part) river, but you end up in amazing rock formations, and you can do the entire hike (as far as the point where you'd need to start rappelling, anyway), up and back, in a day. (The Narrows hike is best done from upriver, but that requires getting a shuttle to take you there and camping for one night on the way downriver.)
My favorite place to stay near Zion is Desert Pearl in Springdale. Nice little hotel with a pool and hot tub, within walking distance of the park entrance.
I haven't hiked down inside Bryce, but I've driven to/through it. Even if you end up not having time to hike there, the drive from Zion to Bryce is beautiful, and it's definitely worth just walking to the overlooks from the parking lots. It looks like another planet.
You're making me want to get back out into my own backyard! That's one of the most beautiful parts of the country in my opinion.
