There are two things that can set this behavior off, well three.
First, have him checked for a urinary infection if you haven’t already. Lots of the time if a cat that normally is well behaved begins having accidents this is the cause. It is painful for them, and they associate the pain with the litter box, and avoid it. Better to be safe and have him checked because in a boy this could cause a blockage in his urinary tract which then turns into an emergency. His bladder could burst.
If he gets a clean bill of health we have to look at the behavioral side. Two other triggers that come to mind are stress (caused by anything from a move, new furniture, new roommate or pet, schedule changes, moving the litter box, anything at all that has changed), or he could be marking his territory. (even though he is neutered, he is still capable of this behavior).
Aside from scooping the box everyday, there are products on the market to help with this. First, you can use a product called 'good cat' which can be purchased at Petco and is added to their water. It is sort of like a St. Johns Wort for cats. Or you can use a product called Rescue Remedy, which is a tincture you can get at health food stores. These will take a week or two to show their effect.
Next, there is a spray called Feliway that is also available in a diffuser, sort of like a plug in air freshener. This emits a pheromone smell that the cat interprets as friendly and in turn he will not feel the need to put his mark everywhere This is probably the most expensive, but also one of the most effective.
Lastly, there is a product called Cat Attract, that you add to that cat litter, also very, very effective, and does the trick most of the time. Also, number of litter boxes, you should have at least one box per cat, and one extra if you have the room. Some cats decide they do not like to pee where they poo, or they may not want to share litterboxes. They should be in low traffic, semi private areas.
Clean all of his marking areas with a product called Nature’s Miracle or any other enzymatic cleaner that is made for the purpose of removing urine odors. This will keep him from being attracted back to those areas. Also, you can try turning one of his areas into a feeding station, as this will help deter him.
I hope these ideas help you. Your case, I would start with a trip to the vet to rule out infection, then proceed with the Feliway, and the Cat Attract if he is infection free. Then add the Good Cat if needed. Give the above a couple of weeks to work. If it does not help, I have another technique that involves a special “vacation” room for him, but I only like to use this as a last resort. Also, another last resort is to ask your vet about a light anti-depressant for him. This can also be helpful in cases such as this, (mostly if stress related), but it can have side effects so it should only be used if nothing else has worked.