i was in znp this past memorial day weekend. actually have some videos i need to edit.
angels landing you can do plus another hike or two. we did it along with the weeping rock. angels landing isn't particularly hard but it gets crowded. just don't do anything stupid and don't rely only on the chains. get your feet set and use the chains as a backup. there's a port o potty near the top but when i was there it was closed.
we did the narrows and it was raining that weekend so it was kind of tough. i'd rent some gear from zion outfitters. At least the shoes because the rocks can be slippery. A walking stick would be very helpful also. make sure to check for flash flood warnings before you start and I'd suggest starting as early as possible. Otherwise it'll be a zoo.
when we went the water was up to your neck at the boulder pair. Funny story but I brought some kid inflatable rings so we could float back downstream but apparently I was too heavy for them. If they worked we probably would have done the full bottom up hike. :
http://www.whitneyzone.com/wz/ubbthreads.php/topics/42567/Re:_The_Narrows_–_Zion_Nationa
If you can get passes for the subway that would be awesome. Most people book those months in advance. When we went a group canceled and unfortunately this girl and her friend got the last two when we were in line behind them.
http://www.nps.gov/zion/planyourvisit/subwaypermits.htm
We did the hidden canyon trail and if you go past the main trail there's a bunch of rock scrambling if that's your thing. If we had more time we probably would have gone for the Observation point trail. Supposedly it gives you the best views. You actually look over angels landing.
This site is an awesome resource for the park:
http://www.citrusmilo.com/zionguide/
When we were leaving some local recommended the Canyon Overlook trail. You actually need to drive to the trail and park in one of the lots nearby. It's a good place to stop if you're traveling to bryce.
http://www.citrusmilo.com/zionguide/canyonoverlook.cfm
If you're willing to drive, I'd also recommend Bryce Canyon. You can see most of the park in a day but it feels almost like you're in a different planet when you're in the canyon. We did a mule ride, which was pretty fun.