Day 1: Zion, Bryce - watch sunset at Bryce. Do a short hike inside Bryce. After that, drive for a few hours and get closer to Arches. stay along I-70
Day 2: Arches - watch sunset at Delicate Arch (quite some hike - not sure if hike opens during winter). stay at Monticello
Day 3: Natural Bridge NM, not very splendid but kill some time so that you arrive Monument Valley in the late afternoon (time for better view). Drive inside the Valley. stay at Cameron.
Day 4: Grand Canyon (enter from East entrance and go all the way to the west end), have a short stop at Hoove Dam at night and back to LV.