Ideas to cover ugly electrical boxes in both corners of my backyard?

They sell faux rocks for situations like this. If that's not to your liking you might buy/build a small 2 or 3 sided trellis and grow a vine on it.

https://www.amazon.com/Faux-Landscaping-Rock-Utility-Covers/dp/B0000UOAJC

Use either lattice or pallets and make a three sided surround. Then it can be a trellis for plants or items can be hung from is as decoration.

I used scotch broom and decorative grass plants around mine and I don't really notice them much anymore. Good luck!

The utility company has the right to remove or destroy anything that is preventing them from accessing the box that they own. If you do anything, make sure it is something that will be moveable so that they can work on it unencumbered. Perhaps a couple of movable pots of plants that would screen it from your view would work. Just make sure it would be something that they won't mind moving out of the way. Perhaps call the utility company, I am sure they would have a few suggestions of what the workers would find acceptable.

i would use a grass like Karl Forrester or Carly Rose and plant about a 8-10 inches away from cable unity box they will still be able to access it

I would pull that green one out to the right of it and plant 3- evergreen trees on an angle cross and that will fix that corner eye sore for you.

Place a sitting bench with a high back to detour their view

Are you handy with wood? Make a bench to place over it.

Or build "surround", paint it.

I have a question, it looks like that green utility box is only about a foot from the fence. I thought several feet of clearance had to be left around these boxes incase they had to work on them? I am getting a fence and mine sets 1 foot inside back property line, city says I can go to line but wondering if I really should or move fence up about 3 feet.

Different utilities have different requirements for this. You need to contact them to find out but generally they want air circulation and easy access.