Truthfully, it depends on what equipment you have, and what period you are looking at doing this stuff.
Here's a few ideas (I don't have experience with ALL of them, so a few of my details may be blurry). Some of them are just daily things that you should be doing in any commercial studio (Cleaning your tape machine)
- Clean Multitrack and 2 track tape machines
- Calibrate same machines
- Check heads to see if they need relapped or replaced, if they do... do it!
- Replace any/all HDs that have been in (heavy) service for over 2 years.
- Clean optical drives
- If you have any vintage mics, get them looked over and perhaps the capsules cleaned (I haven't had this done, but I could imagine a 50 year old U47 might need it).
- Replace worn/microphonic cabling
- Clean the patchbay with solution of choice and methods of choice
- Do the same with any other used I/O panels
- Calibrate all machines that could possibly need it from I/O trims on convertors to the CV inputs on your Eventide 910
- Clean any dustbunnies around powersupplies with fans and such (Digi192 and computers come to mind)
- Clean the computer mouse and keyboard
- Clean your faders as appropriate
- Clean any pots on your console/other gear
- Does your console or other gear need recapped?
- Rehead all drums and tune (yes you can tune drums)
- Restring all guitars and tune
- Get the piano tuned
- Oil the B3/Love the B3
- Tune the Rhodes and any other keyboards that you might have
- Clean any popfilters, and spray with Lysol (away from the mics please!)
- Retube things that need it. Make sure to rebias as needed afterwards.
Defragging your hard drive... I dunno, I never do that to my drives (OS X doesn't really need it that much) but on a PC I know it's a weekly thing at least. There are some things that are really basic like cleaning the glass between the CR and live room that your interns (or you) should do daily anyway. Clean the floor if they aren't clean. Dust will kill your equipment.
Also, maybe this is just me, but each week in a commercial studio, and maybe more this time of year, I like to lysol the whole place wherever people would be touching stuff (light switches, door handles, etc). Colds make your ears useless often, which makes you and your studio useless.
All of these things of course need to be done as they are needed, and not all weekly, and some not yearly even. I haven't seen many good books on studio maintence.