I am American and I am studying abroad in Spain or 89 days. I am not eligible for a visa but I am looking into getting a Spain Residency card. My family wants to meet me in Italy after my program is over. Will I be able to get into Italy with a Spain Residency card? What are the restrictions/what am I allowed to do with the residency card?

Are you even eligible for a Spain Residency card?

As an American arriving on a tourist visa (which is what you are doing) you are allowed in the Schengen Zone for 90 days out of 180 days. BAsed on that, you cannot legally go to Italy.

Can you apply for a residency permit after 89 days?

This is the info required based on a google search:

Non-EU citizens will need:

the visa or visado de residencia obtained from the Spanish consulate in your home country;
proof of financial means;
certificado de antecedentes penales showing you have no criminal record;
medical certificate - necessary for obtaining the visa;
consular inscription;
medical insurance with a company which has offices in Spain;
passport plus photocopy;
three passport-size photos;
payment of fee (not high);
Spanish bank statement showing income arriving from abroad;
deeds to Spanish property or a rental contract, plus photocopy;
completed application form.

The process can take up to 6 mnnths to complete.

I don't think this is a way to get around the 90 day rule for visiting the Schengen zone...

What if I get the Spanish residency card before I go abroad?

Basically, you need a long-term visa (type D), obtained in US before going to Spain, to get any kind of residence permit (residencia). The only other way is if you are a family member of an EEA citizen.

The OP's other thread

http://www.fodors.com/community/euro...is-90-days.cfm