I'm travelling to Romania, Italy, Poland, France and Belgium.
What's the best plan I can get to have data as I travel to these places over the next two weeks?
If you have, or can get T-Mobile Simple Choice plan, you will get free SMS and unlimited (for real) 2G Internet in all those countries as part of your plan. Calls are not free however - they are 20c/min. I've been using this plan extensively around the world, and the only two countries it didn't work at were Nepal and Russia. Nothing special is needed to use this plan, besides turning on your phone, and "Enable Data Roaming" in your settings. You will get an SMS once your phone is up, notifying you that this country is covered under the plan. All the countries you listed are covered.
Other than that, you'll need to buy SIM cards in every respective country to get the best deal. In Romania the cheapest would likely be Cosmotel, not sure about the other countries. It is also possible to buy something like Vodafone in one of the countries (i.e. Romania), and activate the EU roaming, but I'm unsure whether it makes any sense costs-wise, as data roaming is still not that cheap (although way cheaper than it used to be).