So many better trails to ride than Slickrock.
+1 to that. Slickrock is an experience for sure, but you can get that same experience in a lot less time on the Slickrock practice loop and then get a better ride in elsewhere.
J's list is similar to my own, though I think climbing Poison Spider sucks (jeep trail). I would access Portal from Mag7 via Gold Bar Rim (formerly Blue Dot).
So top of my list is basically 3 must-do's - TWE, Mag7, Hymasa/Rockstacker/Ahab.
Just beware that some of these trails are very technical especially Gold Bar Rim/Portal, so if you're not into that you can take an alternate ending - Poison Spider as a descent would be ok, or exit to Gemini Bridges Rd. If you do exit one of those but want a longer ride, climb up a newer trail 7up. For TWE, you won't be able to do the whole thing from Burro this time of year, but if you start at Kokopelli Tr look into doing the newer Jimmy Kean Trail to start. It is a bit more work than Kokopelli which is just a fast downhill fireroad, but JK flows well and is very fun.
A newer trail that I haven't ridden is Navajo Rocks, have heard great things about it. Sounds like it has a ton of variety and not that long at 18 miles for the loop.
There are a ton of other systems in Moab that are worth checking out depending on your schedule and abilities within the group. Moab Brand trails, Klondike Bluffs and Sovereign networks are all spiderwebs of trail of all types and difficulties you can spend all day at, or just a couple hours. For a shorter ride from town Pipe Dream is fun. Also, I have not ridden it but Dead Horse Pt State Park is supposedly mellow (flat) but very scenic.
Arches National Park is nearby and worth checking out in the evening. If you will be there for a week, spending a day in each of Fruita and Grand Junction is worth it for some variety.