Nowadays that's like trying to find work as a mechanic because you know how to change a tire.

I know HTML, CSS, JS, C++, C#, PHP and Hack - and I often can't find work because the bar of competence for many programming jobs still requires knowledge of frameworks, libraries and processes that I don't have experience with, and because the freelance market is global. It can be difficult to tick all the boxes and stand out in a crowd of millions.

1. Learn something that can help you to do stuff that people are willing to pay for. You already know some webdev, so maybe go ahead and spend a couple of months trying out some frontend frameworks. There are ample amounts of frontend jobs everywhere in US, EU and Asia.

2. Find a remote job in US. Even a junior position with a low salary would allow you to live decently in most European places (maybe except downtown London, etc.).

3. Pick a random European city you might like, get an airbnb and just go there for a while.

4. If you like it, stay. If you don't, pick another city. If you can't make the decision in 3 months, move to a cheap place in Asia and go back when you can. Flights are cheap. Places to stay are cheap. Just lower the bar. You don't have to live in the middle of Paris or London this whole time.

5. Travel a lot and profit. Unless of course your prefer to go through a routine of choosing a single place, finding a job in there, networking, making lots of new friends, etc. There's your tradeoff, but hey, you are 26.

[edit: paragraphs]

You can study for cheap and get a student visa in Germany, Austria or an ex Eastern Block country, get a job until senior developer there, then work for a US company.

Forget Italy. Italy is probably nice to live in, but it's at risk of becoming the next Greece right now. Big problems in the banking sector, 1st country for refugees to enter through along with Greece.

Good luck than. Maybe worry about the job, rather than about visa.