Sounds good but be aware it can still have a blizzard at the Grand Canyon late in March. I know first hand!
Like you I am not a gambler, the casinos are amazing there but overall I feel depressed watching the unhappy looking gamblers. Vegas has expensive but many good shows. We always fly to Vegas to get to our western home, but the city for me is too commercial and artificial and we leave ASAP. Another choice is to visit Sedona on your way to the Grand Canyon; fly to Phoenix and drive up through Sedona. Sedona is a magical relaxing place surrounded by gorgeous natural beauty and I know this sounds crazy but I feel a spiritual connection to nature there because of the astounding beauty of the rock formations. A plus is it has good restaurants, but my draw had always been the hiking. Sadly 2 years ago had to stop the hiking with my group of college girlfriends who met up once a year. My darn knees simply won't handle basic easy climbing. Even if hiking is not feasible for you they have the Pink Jeep tours which take you to various gorgeous red rock locations. The drive up to Flagstaff from Sedona is one of the most scenic routes in the US. Reservations are a must at least 6 months in advance if you plan to stay in a hotel or motel, the nicer ones require more than a year ahead in warmer weather. Nothing is cheap there. Phoenix is about the same distance to the Grand Canyon as Vegas is. I know I would not have the courage to walk out on the clear platform, yet it is very popular standing on top of the Grand Canyon. If you do it let us know.