Are both of the following sentences correct?
Let me know if there is still something I need to send to you.
Let me know if there is still something I need to send you.
Which one is more appropriate to use?
Both are semantically correct as they are. But compare
I'll send it to you.
I'll send it you.
The second sentence wouldn't make sense in formal writing, but is found to be understandable in northern England spoken usage. There is also the case of
I'll send you this thing
Which flow much better without the to. In this light it might be more prudent to use send to you, as it is more formal, but send you in your context would also be accepted.
EDIT: I precised my conclusion and added one example following precisions made in the comments.
In addition to what others have said, You can simply find out the difference comparing two sentences: send somebody something
We sent Mom flowers for Mother's Day.
send something to somebody/something
I'll send a copy to you.
Send you is fine: You is an indirect object.
The first sentence is more correct at any time, I will send it to you, send followed by the object to who? I will send the dog to school, I will send him to you. But saying I will send you, sounds I will send you to school, I will send you out.
The verb send must give room to destination, medium of sending and object to be send, and if destination should be specified, it comes at end of the statement. So saying "I will send you books", "you books" (also your books) sounds like a possessive noun phrase and as a whole becomes direct object to the verb "send". according to the aforementioned rule, let us give it a destination (you) and medium of sending (via email), constructively the statement will be I will send you books via email to you. It does not sound good, with following the rule it will be I will books via email to you.
The pattern is: