Hmm. Tough situation. Options for non-US citizens follows very closely with the performance of the economy. When things tighten up, employers restrict the opportunities for international students -- especially those for which they have to the extra mile (e.g., attain Visas) in order to recruit. This changes when the economy is doing well.
The other option you mentioned, going to a US school, but getting an international job, also isn't the easiest to do.
I'd take a look at the schools that interest you as well as companies that interest you and speak with those schools' career services to find out what the companies' policies are right now H1's.