Do you celebrate Easter in your country and if yes, how?
For me, just for my children's sake, I am going into the garden to hide Easter eggs.
For me just for my children's sake , I'm going into the garden to hide ( the ) Easter eggs. You could also say.......... just for my children. Remember, children is already plural ( one child; two children ) children's = belonging to the cfhildren.
For me, just for my children's , I'm going into the garden to hide the Easter eggs.
The first person singular can be "I am going" or "I go".
I think that "I go to the garden" would be more widely used
To celebrate Easter I go I am going  into my garden and hide the  Easter eggs for my children to find.
 The present continuous/progressive can be used for what is happening right now or is going to happen in the future. Indeed "going" is often used for the future.
To describe things that happen more than once or are always true the present simple "I go" is the correct tense to use.
 When speaking generally we usually pluralise and omit the definite article "the". If we use "the" it means that something is unique (or some things are unique) in some way or that the person who is being talked to knows which particular thing is (or things are) being talked about.
Example: I have two sheds in my garden. The  sheds are brown.
 Which sheds are brown? The sheds that are in my garden are brown. In the previous sentence the reader/listener was first told about the two sheds in my garden and now they know which sheds are being talked about. If I wanted to say that all sheds everywhere in the world are brown, I would be speaking generally and I would say...
sheds are brown (no "the")
For me Just for my children's , I'm going to the garden and hide the Easter eggs.
I celebrate Easter, just for my children. I am going to the garden to hide Easter eggs.
You could also say, "I plan to hide Easter eggs in the garden."
Good luck with your English, I am so impressed by all your points on Busuu!!