Any recommendations for inexpensive motel/hotels, not resorts, for May-June 2020?

That's off season & you should be able to find some very good deals on sites like booking.com with ratings, reviews & photos to help you make a choice. For what you want I think that's the most comprehensive way to find it.

Do you have a price range in mind? What do you consider inexpensive?

June is HOT so many (most) properties will have rate discounts. As mentioned - what is your budget . . . and just look at booking.com to find out what's available in your price range.

We like Hotel.com for just about everywhere.

How are you arriving in the Phoenix metro area? When we arrived on an evening flight to Phoenix-Mesa airport we took a taxi to a cheap motel in Mesa and had Enterprise pick us up the next morning. We spent the next 6 nights in Flagstaff which served well as a base for going to Grand Canyon - south rim, Sedona, Winslow and Desert View and a few other places.