I'd go to Lost Coast in the fall, not in the spring. Spring is more likely to be windy and rainy. You may even feel like you haven't escaped the East Coast. The far north coast in CA is COLD.
On the other hand, March is one of the BEST months to visit the desert Southwest. It can be chilly nevertheless, so err on the side of the somewhat lower elevations as Dave C. suggests. (Higher-elevation weather will fluctuate greatly in March. I have been up to Bryce NP (9000+ feet) on a sunny March day and it was very warm. Went there another year about the same time, and a storm took the mercury down to zero degrees at night.) Zion is a great lower-elevation park, and if the weather is warm-ish (or even if it isn't) you can hike quite a few thousand feet uphill from the main valley in Zion up into the rim country. Spectacular.
If it's not too late, make haste to apply for a Grand Canyon permit! March is great timing for a GC visit.
So there is the southern half of Utah, parts of Arizona (GC, Mogollan Rim, Sedona, Tucson, etc.), New Mexico (which I do not know well, and a lot of areas are actually high elevation and cold), and California (Death Valley, Joshua Tree, Anza Borrego State Park, etc.). There are also the parks in far west Texas and I don't know those ones. Lots of choices. However, if someone put a shotgun to my head and demanded to know which of those many great choices is the best trip of a lifetime, there is absolutely no doubt I would choose Grand Canyon and Southern Utah. The Colorado Plateau (which encompasses southern Utah and the Grand Canyon, but not the other places mentioned here) is its own unique, technicolor geography, and no other destination IMO can match it.
Fly into Vegas, rent a car, and those places are a relatively short drive away (by Western USA standards!). Remember too that many of the best places do not happen to be within the national parks.
I get envious even thinking about it!