If "sunshine" is the goal, consider the desert, too. It's closer to the Willamette Valley (are you driving?)

I happen to dislike Las Vegas, but it's a cheap town to stay in a hotel and fly in/out of. And it gets sunshine all winter. Or you could hit Phoenix/Tuscon/ ABQ /El Paso etc, lots of sunshine all around.

Marfa TX is a little arts town in the West Texas desert.

But if it's beach you want, and don't want Mexico (which is pretty cheap, airfare included) I'll second the Aransas idea.

Spring Break in TX starts the 1st week in March, and rolls into April as the northern schools come down.

Creak.