Suggest

I see your dilema, but I'm too tired to say anything intelligent.

Usually, where we have a direct object and an indirect object, the "to" for the indirect object is optional.  But in your example it is required.  I don't know why.

Please give the book to me.  Please give me the book.

Give it to me.  Give me it.(doesn't sound good)

Tell a story to me.(doesn't sound good)  Tell me a story.

Suggest the next step to me.  Suggest me the next step.(unheard of)

Notice that sometimes the one with "to" is the more acceptable one.  Sometimes it's the other way around.

My question is whether it is fine to write 'suggest me- No, it sounds aweful in my opinion  

Possibilities:
Please suggest what I need to do next.
Can you suggest what I should do next
Please give me a suggetion as to what I should do next.


I know for sure it is incorrect to say 'I suggested to you/him on ... ' On the contrary, this may come to you as a surprise. It's quite correct.

"Suggest the next step to me" is fine, but, as you show in your original post #2, the indirect object is not required.  "Please suggest the next step" is also fine.

Again, sometimes the indirect object is required, sometimes not.  The key is the verb and the context.  "How can I amuse the children?"  (reply)  "Tell a story."

"Please give the book" is not natural.  But context could make both direct and indirect objects unnecessary: "This year I cannot afford to give."

BTW Could you please finish your final example in your original post?  -   something like, "I know for a fact it is incorrect to say  etc."