Does this translate to 'I'm not doing anything tomorrow.’？
明日は何もしていませんよ。

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I think that sounds ok.

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I'm not a native speaker by any means, but I think it would be more correct to say:
「明日は何もしません（よ）。」

The reason I think it would be more correct to say しません is because it is an action (or lack there of) that takes place in the future.

For example, would you say, "Tomorrow it will be raining." or "Tomorrow it will rain." 
明日雨が降っている。
明日雨が降る。

Hope this somewhat helps.