At MIT Medical, if there's an internal medicine NP who you do like, you can request them by name, and usually still get an appointment the next day for non-urgent problems. When I got my health care through MIT Medical (I switched insurance away from there recently), I got most of my non-midwife care from Lorraine Toher. I don't like being thrown at the triage pool, either, and I also had the problem at MIT Medical that the doctors are seriously rushed, when it comes to appointments - most will be able to see you for 12 minutes, scheduled three weeks in advance, or something stupid like that.

Also, if you're looking for anything that falls under "well woman care" (pap smear, breast exam, birth control, vaccinations, thyroid test) the midwives are a good bet. The office at MIT Medical is a branch of "Midwives at Mount Auburn", and their MIT office offers regular appointments on Mondays and Thursdays. Like the nurse practitioners (well, which they are) you can latch onto one you like, if you feel like it, though I believe I've met every one of them, and they were all acceptable to me. (Not so for the doctors in ob-gyn.)