Feeding. Without any Food the Fish and Hard Corals wont stay alive for long. I would recommend setting out a feeding regime and sticking with it.
Water Chemistry. Checking water parameters weekly is a really good habit. Keeping them within the recommended amounts by adjusting them accordingly with Buffers and Additives. This will save loads of stress to your Aquariums inhabitants.
Inhabitants condition and health. By spending a few minutes having a really good luck into your aquarium per week can help determine problems and save outbreaks of Disease, Pests, and Algae. These can be early signals telling you that something is not quite right.
Equipment. Checking that all Heaters, Power-heads, Pumps, Skimmer and Computers are functioning properly. Maybe they are ready for routine servicing and cleaning. They may in the worst case need replacing.
Protein skimmer cup cleaning. This must be done at least once a week. If not you might as well just turn it off because it will not function as intended.
Water change. Many Hobbyists recommend a 10% water change every week. But if your biological load is low and parameters check out satisfactory you can do a 20% water change every three to four weeks.
The not so important maintenance includes
Cleaning the Aquarium glass. This is totally for you as the Hobbyist. What would be the point of keeping a Reef Aquarium if you can't see it's natural beauty.
Taking photos. This is a really good way to see the growth of your Aquarium Inhabitants as they grow and mature. Taking a few photos every month is all that is needed. You can show your Family, Friends and fellow Reefers your much loved Aquarium.
Checking and purchasing supplies. As you use your Buffers and Additives you will know when you are running low. What better time and opportunity to go to your Local Fish Shop and replace them. You can even treat your self to a new Coral, Fish or Invertebrate.
This sums up most of the maintenance and checks you should carry out regularly. You will find if you adopt these tips into your Reef housekeeping you should not go far wrong.