Maybe a little late, but better than being silent.
Hi Frank, I grew up in Southern Utah, and have also lived many years in Portland Or. I've cycled extensively in both areas (on road and off) for the last 20 years, including south western Washington and the Seattle area. As an un-roadie these days (last five years) I've been dedicated to exploring all sorts of trails around the country on my dropbar trailbike (CX with 2" tires). If you're interested in riding your CX bike on singletrack trails (hopefully with as fat a tire as you can manage (37mm is a bit thin)), you're in good company. Especially if you are looking to travel with your bike and explore trails across the country, then please join my club (Mountain Goat Bike) here on MTB project. We're a small (but growing) group of of dirty drop bar enthusiasts, looking to share tips and resources to make finding and riding trails a bit more accessible.
As for your question...
While most of Southern Utah is really sandy (anything with less than 3" tires is going to have a hard time with the periodic sand pockets at the lower altitudes) The Zion/Springdale/Hurricane area (outside of the National Park, of course) does have some excellent and very rideable trails. That being said, these trails are going to have plenty of sharp and largish rocks. So, again, I would recommend that you have at MINIMUM 45mm (1.75") tires on your CX bike. While I've not ridden these exact trails enough to give specific advice, I have ridden many similar trails around Kanab and Sedona. Most folks will say that you need a "real" mountain bike to ride these (or any other "fill-in-the-blank" blue or black trail), but they are simply inexperienced in this matter. For these desert trails that I have ridden plenty of, all one needs is adequate skill for handling the short geometry of a CX bike (think "steering with your entire body") and a sufficient pocket of air between rubber and rim, to avoid killing your wheels. Of course, tubeless tires, stout rims, and a beefy fork are all helpful in the likely case that you do bottom out. So.. long story short, I would go to Hurricane and hop on any one of the local trails and enjoy the fun life that god gave you.
Washington is a different story. Much more groomed and ridden. Less jaggy rocks. More roots. More trail diversity. Black means black, as far as big drops and mandatory obstacles. I would stick on the blue trails, unless you are really experienced and comfortable with 18" drops (in general). If you're in Seattle area, Tiger Mountain is awesome, with lots of blue and blue/black options. I've ridden the Tiger Mountain Loop (not including the Predator double black downhill section, of course). That was really quite dooable and enjoyable on a CX bike with 2" tires. All of it.