Time for Grand Canyon is now through May. Best opportunity to score a permit is during the week. Other spots within reasonable distance from Yuma.
Santa Catalina's, Saguaro National Park, Santa Rita's all near Tucson. Plenty of low elevation hiking if there is snow. If not add mountain hiking to the mix (albeit cold)
Mazatzal (see burn area recovery), Superstition Wilderness, Highline Trail all near Phoenix.
Many more places out there, but these I am familiar with. Steve