A dilemma for sure! I'd first check with the utility companies and see what their requirements are. Are the meters read manually or remotely? I'm no garden designer but am thinking a couple of removeable lattice panels painted to match the house might work. Not sure about vines though. The first time someone needs access to the utilities the vines will be in jeopardy. Good luck in your new home!

IMO you might be better off using a wire trellis system so there is no trellis to limit your access to the equipment. Then just plant your bushes or vines in the soil and weave them through the wires as they grow.

I'm not sure you can cover them in vines. You may be able to cover them with a shallow cabinet. Talk to your utilities. If you can't cover them in vines, paint the gray ones white, plant a lovely tree/shrub in the corner to make a focal point.

Another option, if it doesn't violate HOA rules is to paint a mural and the boxes to match. A very simple design like waves or stripes will make utility boxes painted to match disappear.

Bleeding Heart Vines will grow like crazy and don't require much space in the soil

Marie - since you’re in Phoenix - hot hot hot, I seriously doubt anything capable of covering the utility boxes is capable of growing in that narrow bed. Seems like @Christopher CNC idea is the best - rolling panel would allow easy acess to utilities, you could hang something on it as one would do with a wall, & maybe place a big potted something green in the corner at the house. The pot could be easily moved for access too when the panel needs to slide one way or the other. This is a townhouse - your neighbors must have same set up - what are they doing?

I like that rolling panel idea, especially if on the street end of it you can do a hinged version that blocks the view of the utility boxes when approaching the house. Wonder how succulents do in Phoenix. This might be adapted to your home.

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Painting everything the same colour as the wall will make a big difference, and is easy. Cables and everything. The website of our utilities specifically say that it's OK.

Some other ideas. https://www.remodelaholic.com/13-ways-hide-outdoor-eyesores/

go to Wayfair and search "metal privacy screen"

go to Wayfair and search "metal privacy screen"

Love the idea of metal privacy screens, but how much heat will they retain and hold against the stucco? I know you said morning sun, but over 100 degrees F causes things to heat up regardless of sun. Maybe something aluminum will work if you go with a metal screen. Heat buildup might cause issues to the equipment.

love the idea of removable/sliding screen. In the worst heat of the day it will be in shade and metal doesn't heat up anymore than the ambient temperature when not in the sun.

Here are some ideas. I would start looking for a talented carpenter to build something to hide it.

Some smart meters are read remotely, for example our electricity meter. You may not need to leave them open to view for meter reading.

I think the first step is to find out how open these need to be for reading . I have pots on wheels that I use for this same purpose . I must say pretty poor design for sure. Our meters are read remotely but 2 x a year they come and read on site so they need to be able to see them . The pots we have are planted with stuff that allows the remote reading to be done so I checked to see how much greenery would still allow that.

Can we see a photo taken further back?

Not sure what this has to do with desserts.

Maybe she read it as desert?

I would put up some kind of fence. But, if you want to just go cheap, paint all the eye sores the exact color of the house so they will just blend in and not be so noticeable. You could also put plants in front of them.