My wife and I are going to the north rim in April and May. We would like to do several hikes, hopefully ones that let us experience the best of the Grand Canyon's north rim. We are interested in hikes of various lengths and difficulties.
This really depends on what sort of condition you're in. For example, if you're a trail-runner in good shape who's used to high altitudes, the 28 miles from the rim to Phantom Ranch and back would be a reasonable day trip; if you're a sedentary lowlander, even a flat one-mile hike might be hard.
The National Park Service has a list of North Rim trails. If you want to go down into the canyon, there's really only one choice: the North Kaibab Trail. You can follow it to Coconino Overlook, Supai Tunnel, or Roaring Springs in a day depending on your level of fitness (rule of thumb: hiking out takes twice as long as hiking in). For views from the canyon rim, there are various trails ranging from the half-mile Bright Angel Point trail to the ten-mile Ken Patrick trail: pick one (or more).