Drive times below are approximate and from Dubai.
Wadi Shawka, Ras Al Khaimah: about an hour to an hour and a quarter. It is the easiest first wadi: any car reaches the dam and park area, entry is free, and the dam area has washrooms and shaded seating.
Wadi Abadilah and Wadi Bih: both about an hour and a half. What's On puts Abadilah at 1h30, a trail through farmland described as easy to moderate. MyBayut gives about 90 minutes to Wadi Bih via the E611.
Rainbow Valley, Wadi Ghub, Fujairah: about an hour and a half from downtown Dubai, an 11 km round trip of four to six hours through multicoloured layered rock. The Road Reel says a sedan can reach the parking area, no permit is needed, and the small seasonal pools are not suitable for swimming. It lists late November to mid-March as the best months.
Wadi Helo, Sharjah: about 1h40 (What's On).
Wadi Kub, about 1h45, and Wadi Naqab, about two hours, are the two longer drives. Naqab is a hard mountain hike that needs a 4x4 for the final stretch, and Kub is a quiet wild-camping valley with no facilities.
Wadi Wurayah is in Fujairah, about 45 km from Fujairah city. Its drive time from Dubai is not confirmed, and it can only be visited as part of a booked tour.