The internship at Brown Medical School has 4 tracks--neuropsychology, behavioral medicine, adult, and child (general and pediatrics). Both the adult and the behavioral medicine tracks are "ACT friendly." I know less about the child tracks--others might add their input about the child rotations.
In the adult track, there is a women's partial program that trains in DBT, and interns familiar with ACT have mentioned that they gained a better understanding of ACT principles through this rotation. There are also some people familiar with ACT in the alcohol center at Butler Hospital and at the RIH inpatient rotation (mood disorders rotation).
In the behavioral medicine track, there is one rotation (RIH behavioral medicine track--anxiety and sleep disorders) that is very ACT friendly. Both of the Miriam rotations (A and B) are also open to ACT and mindfulness concepts (chronic pain, weight management, smoking cessation).
Overall, the internship is hospital-based, and 4 hrs/week are reserved for research. You are required to submit at least one research project by the end of the year. Keep those details in mind when applying to make sure it's a good fit aside from the ACT friendly rotations.
Added by Kristy Dalrymple on 7/23/2013:
In addition to the information here, the predoctoral internship at the Alpert Medical School of Brown University also has a MIDAS Project Clinical Research Track (a separate track from the Adult Clinical track, yet under the adult division). The MIDAS track (which stands for the Methods to Improve Diagnostic Assessment and Services Project) typically has one internship slot available per year, with potential opportunities for a postdoctoral fellowship. Interns in this track spend the first 8 months (20% time) at an ACT and mindfulness-based partial hospitalization program at Rhode Island Hospital, including conducting ACT and mindfulness-based group and individual therapy sessions. Note that the primary rotation consists of 50% time clinical research, and applicants should consider this when applying to the MIDAS track.