If you still have affairs in Spain or you plan to visit regularly, I would advise against closing your account there unless it is expensive. I still have a bank account in the Netherlands and it simplifies at lot of things to have it.
I would recommend you take enough money to get you going in the US with you but leave the rest in your bank account in Spain. Once you have opened a bank account in the US, use a foreign exchange transfer service like ofx, XE trade or Transferwise to transfer the money to yourself.
In general, foreign exchange transfer services are the most cost effective way to transfer money internationally (much better than your own bank, Pay Pal, Western Union, wire transfers, etc). They are "fast" in that it can take less than a week to transfer money, but other methods are faster if time is of the essence.