If your passport (or even your national ID card) has a residential address listed (like the French passport/ID) then write down that address. That's what I do in the many countries that I travel to that require an address. The fact that this address may or may not be valid is beside the point. It's on the passport, it's official... :-)
If not, write whatever address you last had. It's not like they are going to check, unless you are from a country that is on their shit list. But in that case, you probably don't get visa-free entry, and would have to apply for a visa, where you'd have to provide an address...
The probability that their administration will want to contact you is very small -- and generally that would be while you are in-country, which is why they ask where you'll stay. And they can reach you at the border if they really want to talk to you.
Likewise, unless you're facing a very suspicious immigration officer (and your attitude justifies their suspicion), you won't have to prove your address. Never once, in close to 30 years of international travel, have I been asked once to prove my address at a border. And I used to carry a backpack and had long hair too! Now, not so much of course...
Bottom line, write down your last address and forget about it.