Is your goal to be in the US, or is your goal to not go back to your home country? Those are two different things.
Australia and Canada have excellent universities and immigration policies that are much friendlier than the US. Look at both of those places.
Do not come here with the goal of staying here. The rules are constantly changing, and utterly irrational.
@tarator - Yes some recent graduates do manage to score H1B visas every year, but those individuals are rare exceptions. Most of the H1B’s go to people with multiple years of work experience in specialized fields.