How should I cover this drainage garden pit in my front yard?
Those typically act as temporary rain water water storage tanks. The idea being to limit the demand on the sewer system during storms. The water is allowed to back-up in those pits and drain more slowly to the sewer system. They may also be used in high water table areas to collect and drain the water table before the water enters your house during the rainy or snow melt season.

You have a few choices. 

You could fill it with rocks, but that would take away a lot of volume and defeat the purpose of the pit so I do not recommend it. That may also be against code in your area.

You could cover it with a grating, perhaps made from metal fencing materials or a custom grating, but that wont look that wonderful and is a pain to clean out leaves, blown in trash, or someone's cigarette butts...grrr.

You could, put a fence around it to stop folks from falling in, but again, that's a bit of an eyesore and the cleaning issue.

Personally I'd cover it entirely, leaving an air hole in the side and access to the maintenance pipe cap shown in the image. Perhaps composite decking or some other material, then make a feature out of it with planters.

My personal, preferred solution would be to turn the "decking' into a box, that is make the entire decking one big attractive planter over the open box. Would be a fun project too :) I'd make the sides of the box match the cladding I see on the wall behind. I'd also extend the maintenance pipe up through the box so you can get at it without having to remove the planter. Maybe have it end just under planter soil level.