Night Elf to Ironforge/Stormwind City
There are two routes to Alliance territory: for both, start by taking the boat to Menethil Bay in the Wetlands. Of the two, the road route is better and much faster.
The much shorter run is to head along the road (generally in an eastward direction) to Dun Algaz. Mobs on the roads are 22-23 or so, and mobs in Dun Algaz are 20+, but should be avoidable or outrun with care. Enter Loch Modan at Algaz Station (that’s the North gate pass from Dun Morogh). There are griffon masters in Menethil Bay, Thelsamar (in Loch Modan), and Ironforge. While you are there, take the tram to Stormwind and learn the flight path as well.
Or: from Menethil Bay, you can swim south. Stay far out to sea, on the edge of the fatigue line, as there is a camp of murlocs just west of the harbour; I am not sure if this will succeed or not, but it stands a better chance than running along the shore. From there, you eventually swim in and out of Wetlands, Dun Morogh, Westfall and Stormwind City, ending up on the north beach of Westfall, from where you can learn the flight path at Sentinel Hill and run to Stormwind City. This is a very long and tedious swim, utterly devoid of mobs until you hit the beach. There are several places where you can climb ashore, but none break through to the interior. It may be possible to swim out to sea to die of fatigue/drowning, and respawn at a graveyard in one of these zones; but it seemed most likely to me that you would end up back in the Wetlands.
Once you know the way:
Start in Auberdine, Darkshore; take the boat to Menethil Bay, Wetlands. From there take a flight to Ironforge. Optionally take the tram to Stormwind City, but you are probably taking this route to get to the auction house. Reverse to get back – or use your hearthstone.
Night Elf to Booty Bay
Take the boat from Auberdine to Menethil Bay, Wetlands, and from there the boat to Theramore, in Dustwallow Marsh. Short run north into the Barrens. Alternatively, run south from Ashenvale into the Barrens, and take the boat from Ratchet to Booty Bay.
Others
Not many journeys are quite as epic. A low level tauren can relatively easily reach Orgrimmar, and thence Undercity, by simply running from Mulgore into the Barrens and then Durotar. The same applies in reverse.