For a quick escape, dip into Three Dog Bakery. They have a fantastic selection of treats for your dog including ice cream-flavored wafers plus all sorts of fun takes on human favorites and the store is kept cool for the sake of the baked goods.
Just like the insane amount of dog-friendly restaurants that exist in many parts of New Mexico, there are nearly just as many hotels, some of which are surprisingly upscale. You can just as easily find something cheap, or try Airbnb as well, but being in a new place even just for the hottest parts of the day can be a great escape.
If you want a really special gift for yourself or a loved one that will last a long time, consider stopping in at Back at the Ranch Cowboy Boots. They make custom boots with whatever kind of imagery you want, whether that's your dog's favorite spot or your favorite dog!