Don't hesitate just do it ! I did a trip there sometime ago before diagnosis but i think I could still do it now as long as I allowed myself to be a little slower . The canyon lands aren't at especially high altitude and I don't think altitude especially affects Parkinsons more than any one else . I 've not noticed altitude effects in the USA ,I have done in the Andes in Peru/Bolivia and the Himalayas in Nepal /Tibet but their much higher places and for long periods high up to . I think I have read some where that Micheal J Fox felt his symptons were better whilst at altitude in Buhtan !! I was in the mountains of the south island of new zealand last month the only thing I noticed was my tremor being worse on exertion on steep paths , I had worried about my left leg coping with rocky paths but it did ok .I am in early stages so working on Bucket list too before I can't .In the canyonlands you will be able to see alot with out having to do to much exertion my favourite was Zion national park I remember a steep walk there up angels landing which might be harder now but you would still see alot without doing it .The canyon lands are amongst the most diverse landscapes in the world the american national parks service maintains very good access to them ,they are the best national park service in the world in my opinion .Take a good camera and good size memory card Bryce was great as is monument valley , Whytes canyon and of course the grand canyon all accessible at level of exertion that suits you .Thinking about it I have also read of people with PD doing the Inca trail which is alot higher in altitude and exertion !! Have fun .