I've been predicting the bursting of the housing bubble in Kiev fto happen anytime for a couple of years now and it just doesn't seem to be happening. There is still enough foreign speculation there to keep it inflated. Apparently it is following the trend of other FSU countries in that regard, and those markets haver seemed to maintain their increased values. Still, I would be hesitant to buy anything longterm right now in Kiev. In other areas, though, it's not so extreme and, even though you can't get the deals on housing that some of us were able to get a few years ago, there are still some good affordable properties. You just need to know how and where to look.
With regard to the other areas mentioned, the price of food has indeed gone up, so if you intend to live and eat like a Westerner there, there won't be much of a reduction in food costs with the move. If you do like we do, which is grow much of our own at our dacha, buy fresh produce from the local market and cook it yourself, you can live much cheaper. Even with the increase in prices, I think one can eat cheaper and healthier there.
As far as the medical care, even with the added price for extra care, it is still MUCH cheaper than in the US. For example, we recently went all out for a kidney operation for my MIL and the total cost was $6,000 compared to around %40,000 for the same care in the US.
Gasoline prices are not an issue if you use the mass transit system, which is very cheap and convenient. We lived downtown so everything was easily accessible by foot or marshrutka. For out of town trips there are buses and trains. We share a care with our in-laws for special trips.
Where one saves money is through no income tax, no health or auto insurance, no mortgage, no car payment, lower entertainment costs, etc.
In other words, despite the inflation, it is still possible to live much cheaper there if you are willing to make the necessary compromises.