Where can you go to get your passport in less than a week?

I don't know about "less than a week", but there are about 30 US Department of State Passport Agencies scattered about the country (see related links). You can, based on need, get expedited service from one of them. When I got my first passport, I needed it for a business trip that came up suddenly where I was leaving in literally three days; I went to the agency in Boston early in the morning, gave them the forms and proof of citizenship they needed, and went back that afternoon to pick up the passport (I'm not sure that level of service is still available). I then had to drop it off at the Boston "Taipei Economic and Cultural Office" (calling them "consultates" ticks off Red China) for a visa and return the next day to pick that up.

Outside of that, the fastest option is expedited service by mail: about three weeks.

There's an extra fee for expedited service either by mail or at an agency.