Trauma Centers have to reach and maintain certain standards as designated by the American College of Surgeons Committee on Trauma (ACSCOT):
Prior to applying for state certification, Level I, II, and III trauma centers must complete an application to ACSCOT and have a verification visit by a team from ACSCOT. Using ACSCOT criteria, Level IV trauma centers are verified by a state team.
Level I Regional Resource Center Level I Trauma Centers generally serve large cities or population-dense areas. A Level I Trauma Center is responsible for providing leadership in research, professional and community education. Must have neurosurgery, general surgery and orthopedic surgery available at all hours. All have systems in place to transport patients into their center (ie, helicopters).
Level II Regional Trauma Centers A Level II Trauma Center provides comprehensive trauma care and serves as a lead trauma facility for a geographical area. A Level II Trauma Center provides educational outreach and prevention programs and assumes responsibility for trauma system leadership. There are emergency physicians and nurses in-house to initiate resuscitation and stabilization, with surgical teams on call and promptly available.
Level III Area Trauma Center The Level III Trauma Center provides assessment, resuscitation, emergency surgery, and stabilization and, for the most critically injured patients, arranges for transfer to a Level I or Level II trauma center that can provide further definitive care. A general surgeon must be promptly available and the facility must be involved with prevention and have an active outreach program for its referring communities.
Level IV Local Trauma Stabilization Center Level IV Trauma Centers are small rural facilities that provide initial evaluation and assessment of injured patients prior to transfer to a larger referral facility.
Here is a link to a list of trauma centers verified by ACS (note that not all trauma centers, including Level 1s, are included on the list, only those which have applied for and received ACS verification):
http://www.facs.org/trauma/verified.html
In regards to your surgery rotation, while it sounds great to do surgery at a Level 1 trauma center, what is most important is where you will get good teaching. This is not necessarily at a program which is top heavy with residents and fellows. So the above list may help, but do not discount Level 2 centers or non trauma centers as places to do your surgery rotation.