Going Towards a Tsunami

Say I had a 30 minute warning that a tsunami was about to hit the coast. Would it possible for me to swim or boat out into the ocean until I got sufficiently far away from land that the only thing I feel is a slight bump in sea level? How far away would that be, how would the strategy compare with heading for the hills instead?

No idea for your first question, but as for the second, I would certainly head inland. On Sky News this morning the editor of the Phuket Gazette was trying to convince people that they could still holiday there. Apparently the farthest the waters came inland was 300 metres. Given 30 minutes warning you should be able to get far enough inland to be safe.

It depends on a number of factors; including the magnitude of the incoming wave, how steeply the sea floor slopes downwards and ‘funnelling’ effects from locall headlands. If you’re on a stretch of open coast where the sea floor ‘drops off’ significantly and abruptly a little way off shore, you’ve a much better chance of reaching deep, mostly unaffected waters than if you were, say, standing on mud flats in a large estuary.

The problem isn’t necessarily the initial impact, but also the devastation that it causes, which will result in less-than-stellar living conditions for a while. Roads out, food scarce, disease, breakdown of order…

If you’re going out to sea to escape a tsunami, don’t bother coming back for a while.

This is probably true in Phuket but not Khao Lak, where a lot of the missing and killed were in Thailand. A couple of factors there, but the main one is probably the topography. Phuket is a large island ringed with beautiful beaches, and lots of large hills (almost, but not quite mountains IIRC). So the incline from the initial beach is usually somewhat steep. At 300 meters inland you’re already pretty far up a hill in most parts.
As to the OP, I heard a report on NPR of a guy who runs an orphanage getting a bunch of kids into a boat and heading into the wave. Now the guy sounded a little loopy to be fair, so not sure if it was true. I suppose if you didn’t capsize from the initial wave you’d probably be okay. I doubt that swimming would work, the undertow would have to be enormously strong when the beach waters rushed out.