Here's a good way to know when it's time to PCS: You drive more than 6 hours to see new things on a long weekend. That said, we have started to venture further and further from home base on long weekends. But just because this weekend trip was to Utah doesn't mean it's any further than California destinations.
In fact, Zion National Park ($25 for 7 days) is closer to Edwards AFB than San Francisco. The 370 miles to the park will take you 6 hours (no kids) but is well worth the trip on a 3 or 4 day weekend. There is only one hotel and accompanying restaurant in the park: the Zion Lodge. It looked 'average,' so find more value for your dollar in the towns just outside the park gates (Springdale, Rockville).
Break up your drive to Zion by laying over at Nellis AFB for a night or by going by way of Pipe Spring National Monument. Pipe Spring is a quirky old Mormon ranch, co-located on a Native American reservation. It's said that Stephen Mather (NPS Director 1917-1929) added the monument only because he broke down en route to the North Rim of the Grand Canyon and the residents helped him out, subsequently telling the history of the ranch.
We stayed at the Dream Catcher Inn in Rockville. The inn's breakfasts were splendid and the room was ample. It's a fun 10-min drive from Rockville to the ghost town of Grafton, UT (cross the iron bridge on Bridge St and follow the signs). And make sure to pick up a sack lunch at the Springdale Fruit Company on your way into the park. In season, they also have U-Pick apples in their orchard.
Plan 2-3 days in Zion. It can be seen in a day, but you'll want to experience the outer stretches of the park to really get a feel for the majesty. A great half-day hike goes to Angel's Landing. Shorter options include loop trails to the Emerald Pools (hanging garden on a sandstone face), the Pa'rus trail and others. During peak times, the park road only allows shuttle buses. Park at the Visitor's Center and embrace the service. A secondary Visitor's Center (a couple stops up the park road) has a great 22 minute film on park basics.
The park also has a road running from just north of the main Visitor's Center to the East. It goes thru an old tunnel (longest in US when it opened) into a completely different zone of the park. You can see the famous "Checkerboard Mesa" and hoodoos on this end of the park.
For a truly spectacular memory, hike the Narrows. You'll need canyoneering shoes (or close toed shoes) and if it's cold, dry-pants, a walking stick and neoprene socks. We rented our entire ensemble from the Zion Adventure Company for $35 and admit it was worth every cent. You can do a "top-down" one-way Narrows hike, but we chose the "bottom-up" out and back. This route starts at the end of the shuttle bus line (Temple of Sinawava). You suit up and walk 4 miles up the Virgin River. Depending on the water flow, you could be up to your chest in water. The day we hiked the Narrows, there was a 67 cubic feet per minute flow rate in the river and the water was around our waist or lower. The Narrows is a slot canyon, so the walls rise very high on both sides of you. It's truly a magnificent site - especially in the area titled "Wall Street."
For those more adventurous, you can try the Subway hike - but that'll involve a little more planning.
Zion is 6 hours away and the neighboring Utah parks (Cedar Breaks, Bryce Canyon, etc) are even further. But for Nellis or Edwards folks, it's a great place for outdoor adventure.