My interest was tweaked when I kept seeing an unusual little day hike on “best hikes in Utah” lists.
The name is surprising too: Negro Bill’s Canyon. (I will lobbyinglobby for a name change to Mitt Romney Canyon if he wins the Presidency in 2008.)
It’s popular for a number of reasons:
Despite the plentiful poison ivy, this is a very popular hike for those owning dogs and/or children.
Ultimately, it’s a nice change from the dry, hot desert environment outside the canyon. And 3.2mi (5.15km) is a nice distance for a short walk.
Morning Glory Natural Bridge … or, more accurately, …
This is not a natural bridge, but it is a very large alcove arch. Robert Vreeland measured the span of this arch and reported it to be 243 feet in Volume 5 of his book series, Natures Bridges and Arches. This volume is now out of print. Jay Wilbur of NABS has confirmed this measurement.
besthike.com 
Sounds like you really enjoyed Moab and area!
You can also do Negro Bill Canyon from the top by canyoneering a ways above Morning Glory Arch, rappelling of it, then hiking out through Negro Bill. The route starts up past the SlickRock bike trails.
Makes for a great adventure!
DSD
“Summit Stones & Adventure Musings”