You might consider looking for companies that really interest you, and you can directly email their recruiters. As a student who has had my fair share of internship hunting, I find it more reliable to go hunting for what interests me rather than hoping something interesting happens to show up. Opportunities do just show up(linkedin recruiters sort of thing), but it's just a far lower chance that those turn out to be as interesting as companies that I scouted out on my own.
And if you wait two days from now, it'll be May, and you'll find a fat list of companies who might want to hire you two as interns in the 'Who is Hiring, May 2012' posting.
However, most startups won't be certified as a J-1 sponsor, so I can help there through working with USCIS, make sure the process works out.
Have you checked to make sure that J-1 won't require you to spend two years physically in the Czech Republic before applying for another visa? http://j1visa.state.gov/participants/common-questions/ (check tax and immigration requirements)
I have an email in my profile if you want to talk more.
As a student in a similar situation, but from Canada, I'd add the suggestion of looking for teams you would genuinely love to be apart of, and targeting them.
Why?
Say you find five or six places that are tackling a problem that really excites you - and a team of individuals at each of these places, that as a student you can feel welcome to work your butt off while gaining a tonne in knowledge and wisdom.
Build something for each of these places - and personalize. Show that you give a shit about the problem they are solving.
As a recent graduate with a few internships under my belt, I have seen plenty students come from abroad for internships. Although this was an awesome idea, I think it might only target smaller companies that do their own recruiting. Even for the smaller companies, this might not be the "best" approach. I agree with doing something more custom based for them to show that you are passionate, although it would be a much more time consuming process.
On the other hand, the bigger companies will want you to apply more directly.
David is from CVUT/Open Informatics - http://oi.fel.cvut.cz/en/home. I'm not sure about Tomas. I met him some time ago when they were working on a web app with David. These guys are really passionate about building things on the web, that's for sure :)
Would you mind getting in touch? My mail should be in my profile. It's always nice to meet people from HN in Prague :)
There are more types of J-1 visas, version I know about is to get a job offer fist, signed by US employer from some restaurant or other seasonal work. Its summer work and travel program. This is the easiest way to come and work for summer legally if you are regular student.
I spend last summer in California on a J-1 work travel visa (Irish student). I had no job lined up before I went over and the visa was very easy to get. Agencies do all the work for you for a reasonable fee.
Some places to start: http://news.ycombinator.com/jobs Or these: http://news.ycombinator.com/item?id=3783657
And if you wait two days from now, it'll be May, and you'll find a fat list of companies who might want to hire you two as interns in the 'Who is Hiring, May 2012' posting.