Zion - hike the Narrows if it is open (might not be in May due to high flow rates after spring melt) - it is such a unique hike and definitely my favorite in the park! Start early and you will have the river mostly to yourself on the way out - you'll dodge crowds on the way back. The West Rim trail (top down) is a good option if you want something longer - you'll have the option of adding on Angel's Landing, but it will be during "peak" tourist time. I shuttled to the trailhead with Zion Adventure Company. Saw essentially NO ONE on the trail until we neared Angel's Landing - though there are backcountry sites along the route so a few people should have been around. Observation Point is also a great hike, much less crowded than AL (and you get to look down on it at the end), especially if you start early. I loved the views all along the hike.
Bryce - 3 days is probably too many, I'd add some of this time to Zion. I spent 2.5 days earlier this year, and it was a little too much as the scenery everywhere started to look similar. I think the Fairyland Loop was my favorite (no crowds), but I also did the "Figure 8", which was more popular. The horse poop on the Peekaboo Loop section was not fun.
Arches - I really enjoyed Arches, though most of the hikes were of the shorter variety. Delicate Arch for sunset was pretty neat - it was crowded but not annoyingly so. My days usually consisted of getting out for sunrise in the morning, leaving and taking a nap mid-day, then returning before sunset.
Canyonlands - Needles - I loved the Chesler Park Loop - I don't think it would be too long of a day given your hiking speed. I'm slow, started out with a morning "hike" at the Windows in Arches, and still finished way before sunset.
Natural Bridges - This was a great stop, too. I had intended to do the full loop using the trail that connects all 3 bridges, but the trail was so overgrown at the bottom that I abandoned that idea, and just hiked down to each bridge individually.
Grand Canyon - No advice, since I'm doing it in a few weeks North-to-South (as noted above North Rim doesn't open until May 15 each year). My plans started out trying to add a North Rim visit to my Zion/Bryce trip, but it's still pretty out of the way from there. Somehow I just decided to make a separate trip and go all out with a rim-to-rim. It sounds like you have the ability to do rim to river and back in a day - if that is the experience you want. I'm personally spending 2 days at Phantom Ranch so (hopefully) I can enjoy spending some time at the bottom of the canyon.