Is Ukraine the sort of place to arrive without a plan or even a map?

Ukraine's certainly cheaper than Lebanon.

However, language will be an obstacle. Unemployment is high and you shouldn't count on getting casual farm work.

Depending on your passport you may need to get a visa which requires advance planning.

The language barrier for an English speaker is very high in Ukraine. (Much higher than Lebanon, though maybe on par with Syria for a non-Arabic-speaker or Turkey-outside-Istanbul for a non-Turkish-speaker.) I think you can travel in Ukraine without in-depth planning, and I think you can travel in Ukraine without speaking Russian (awkwardly), but I wouldn't do both at the same time.

The language barrier for an English speaker is very high in Ukraine. - It is true for little towns and villages not for Kiev.

"Is Ukraine the sort of place to arrive without a plan or even a map?"
That's exactly what I did.

Creative ways to travel and live cheaply, eh? How about FREE?
You can try some of the thing I did in Ukraine.
For a few day I slept on a building's roof top (in summer).
Then I hooked up with a female college student and slept in her dorm room for 2 weeks.
She fed me with 2 big sacks of potatoes she brought from her village. God bless her.

"I don't speak any Eastern European language. "

Neither do I. Don't worry you'll be fine. Just use common sense and a little street smart.
Money is the international language that all people understand.

Money is the international language that all people understand.

The OP makes it clear, however, that he doesn't speak that language either.

In Western countries I can couchsurf.

If you couch-surf in Western countries, what's to stop you from couch-surfing in Ukraine? Couchsurfing.org has thousands of Ukrainian users.

Language is much more of an obstacle than it is in Western Europe, but hardly insurmountable. You're likely to have an extremely difficult time, however, finding the sort of informal, under-the-table work opportunities you describe in the OP.

Few Ukrainians speak anything but Russian and Ukrainian. Some of the younger generation are learning English, so if you need to find an English speaker look for someone under 30 and hope for the best. This can make travel a bit of a challenge as nobody who sells tickets for trains, buses, etc. will speak English.

I tend to be skeptical about reports like #4's. I suppose anything is possible, but I wouldn't count on that happening to you.

Ukraine in general is not a budget destination and there are few cheap places to stay. I've heard of Ukrainians who supposedly allow foreigners to couch surf and I suppose it's possible, but you should also understand that in very general terms the average Ukrainian is not really interested in doing someone a favor without getting something back for it. Maybe you'll go and stay and eat for free at a bunch of different people's apartments and then again I could also see that you couldn't find anyplace to stay except hotels and you will not like what most hotels charge in Ukraine.

Each person is different in terms of what they like and don't like, but in my opinion Ukraine's smaller towns rarely have anything of interest for travelers and if you can't speak Russian or Ukrainian, it may just increase your sense of boredom and isolation. The southern part of Ukraine east of Odessa and north of the Crimea is an industrial region and it's pretty dreary for the most part. It would not be a place I would recommend to tourists.

Путешествовать можно Украина исторический центр Христианства Поломник - может это твой способ посмотреть Украину