That is not a cheap old rundown shack of a house. It looks like a really nice new one that cost quite a bit of $$.

I would bite the bullet, pay the money to have the power put underground and to move that hydrant.

That's what I would do.

I'd have to agree hoovb. Because they limit you to like 10 feet or so of doing anything near the utilities...it's still going to stand out! Yikes!

Beg for forgiveness - don't ask for permission...
A much cheeper solution would be to make a nice berm under it to cover up the black bit. Then plant the berm with thick bunches of yellow colored flowers and maybe a dwarf nandina or two for evergreen appeal. Make a defined gravel path from the side or the back of the path up to the hydrant with a least a two ft. clearance around it... Oh and don't get mad if the fire dept. tramples all your plants when they're trying to save someone's house.
{{!gwi}}

I would call the city and have them lower the hydrant. It is way too tall. Then, do the plants!

The fire hydrant MUST be accessible at all times, or you may face a liability. Check with the authorities.

However, one could use a lower growing plant like an orange lily.

When I built my new home, I discovered to my dismay( after paying for the house) that there is an above ground electricity transformer, a cable splitter box, and a telephone splitter box on my front yard, so I can truly appreciate the dismay of above home owner. I planted miscanthus sinensis malepartus around the cable and telephone boxes, and orange lilies in front of the hydro transformer. It is not quite so imperative that these not be hidden as the fire hydrant. It would be a shame for the fire department not being able to find the hydrant if they needed to fight a fire at a neighbour's home or your home. Tell the home owner to ask for a reduction in fire insurance, and they should get it.

You can paint the guy wire collar, but you can't paint the hydrant. In my area the color of the hydrant indicates the pressure and flow rate of the water line that feeds it. Very important to the Fire Dept.
I would define the lawn shape and plant the area in question to trees and evergreen shrubs leaving access to the hydrant from the street and plenty of room for the hydrant to be opened with a hydrant wrench. Then Fire Dept. will be glad to give you the information and may even show you.
Right now the lawn covers way too much space and needs to be shrunk. Keep it up next to the driveway and sidewalk for convenience sake and think of the shape of the lawn as if it were liquid. Leave plenty of room for planting beds. Most people make them too small and then have to either enlarge them later, or trim the plants to the point they look butchered. The lawn shape takes priority over the shape of the planting beds, rather than other the way around.
Hope this helps.