If you heart is set on the the US your best bet is to to obtain a student visa and go to university. You may have to get student loans to help pay tuition and board but you can offset the cost and maybe pay for every thing by working at the university either in administration, the bookstore, as a teachers aide, etc. This is the only legal work option for international students while in school. After earning a degree you will be allowed to stay in the states for one year and can work at any job. After that you will need a US company to sponsor a visa to work longer. If you are good at math and science I would recommend engineering or science degree. These two fields are some of the highest in demand in the US and you will have the best opportunity of finding a job after graduating.
As for area I would look at the Southeastern US. Warm pleasant climate, affordable living and also supports growing industries and an expanding job market. Take a look at Jacksonville, FL, Atlanta, GA, New Orleans, LA, Memphis, TN.
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