I luckily haven't experienced spider mites, but I wanted to take my brand new AOS Orchid Pest Guide out for a spin!
If you wanted a biological control, the predatory mite Phytoseiulus persimilis chows on spider mites, and then itself dies off from starvation after the spider mites are history. Of course trading one form of vermin for another in your apartment may not excite you...
The other non-greenhouse suggestions listed are:
Avid 0.15 EC (emulsifiable concentrates) - see lable directions;
Insecticidal soap - see label directions;
Mavrik Aquaflow - 5 fl. oz.
Hope this helps!