I'd like to throw in another perspective — a ninth suggestion, perhaps, which I contend trumps all others:
Do nothing at all.
If you find yourself fidgety and in need of distraction in the mere two to three minutes during the magical marriage of tea leaves and water, then you really do need a cup of tea. Not for the relaxation that may come from its actual consumption — the warmth, the theanine — but from the lessons that come in the simple act of being still. These moments are a gift, a blessing. They bracket a little bit of peace within the rest of your day. Don't schedule them, seize them. Stand, sit, stare into space.
Hearken back to this splendid post, a wise instruction manual called "How to sit in a chair and drink tea" (which I celebrated earlier), and its crucial observation about the steeping moment: "You will now confront one of modern society’s ever-present dangers, which is the risk of distraction we face whenever nothing interesting happens for a few minutes."
Let nothing interesting happen. Let absolutely nothing happen. Modern life is too much happening. The tea is happening, and that's enough.
From my favorite Kafka aphorism:
Remain sitting at your table and listen. Do not even listen, simply wait, be quiet, still and solitary. The world will freely offer itself to you to be unmasked, it has no choice, it will roll in ecstasy at your feet.