"send your letters to me" or "send me your letters"

Both are ok.

The only time (at least that I know of) you can't use the second kind of construction is when the thing somebody is giving away is expressed with a pronoun. For instance:

*Send the old man it.

Both are correct. There is no difference in meaning between the two, but there is a slight difference in what is being emphasized.

"Send your letters to me."
The emphasis is on what ought to be sent. In this sentence, "your letters" is the object of the verb "send", and "to me" is a prepositional phrase that acts as an adverb modifying "send".

"Send me your letters."
The emphasis is on the person to whom the letters ought to be sent. In this sentence, "me" is the direct object of the verb "send", and "your letters" is its indirect object.