Pick a focus. You can't do it all on internship, or in your professional life. There's a reason most clinicians aren't researchers and most researchers aren't clinicians -- either occupation takes full-time effort.
If you want to work in a hospital as a psychologist, your best bet is to work in a hospital on internship. This is pretty much the standard for anyone -- pick an internship that is consistent with your overall career goals. No point in working in a university counseling center if you have no desire to do that as your career (although a practicum rotation in one can't hurt).
Having said that, it's been my experience that VAs are great hospital environments to work in in most locales. Psychologists are well-respected in most VAs, and are given as much due as medical doctors.
John