What is the best translation of ''address'' in this context?

When asking people's mailing address, 住所 is the correct word. However, instead of あなた, you should use your penpal's name and title, or perhaps a nickname if you have been using one before.

～さんの住所は何ですか。

It would be even better to ask it a bit more politely:

～さんの住所を教えていただけますか。

Be sure to know how to write your penpal's full name on the envelope correctly.

アドレス would work but it is more of an IT term. 宛先 refers to the destination of the letter whereas 表書き stands for what is written on the envelope. 所番地 means an address but is not as commonly used as 住所.