Hi, if you have an N.I.E. and a physical address you shouldn't have any problem opening a bank account.
Obviously you'll need to read the small print of all the banks — especially with regard to incoming and outgoing international transfers.
For example, my partner is a U.S. citizen with a U.S. tax and social security number — she's lived here for 40 years, pays taxes to the IRS and Spanish hacienda, and banks with La Caixa — for every outgoing transfer of funds to the U.S. she pays 15€ for amounts up to 10,000€ — beyond which they charge 1.5%. She also sometimes has to pay a fee for incoming transfers from the U.S. depending on which bank is making the transfer.
I bank with ING — ( I have an ITIN — U.S. international tax number — as I receive business payments from the U.S.) and all outgoing international transfers are free of charge up to 15,000€. Incoming transfers — nil. (less 5% to the IRS*). I have never had reason to transfer more than 15K so, for me, all good. Your needs will be different.
* I'm a Brit — and a European citizen until December 31 this year. However, the Spanish 'convenio' with the United States requires I have to pay 5% of my U.S. earnings to the IRS. (If I resided in the U.K. it would be 0%)
Enjoy your time in Barcelona.