Hello,
Yes I would trim away any obviously damaged foliage, being careful to make the cut just above a leaf node(joint). I would also remove flowers and buds Pelargoniums are half-hardy perennials that will, in my experience, survive in well lit cool situations. The minimum safe temperature is about +5 degrees celsius or 40 degrees Fahrenheit. I would opt for the basement. Keep the plant roots fairly dry but do not allow the plant to wilt. If you encounter a spell of very cold weather you should consider supplementary heating.
Hope this helps
Ron

Linnea, you have two options....either keep them going as you are doing or give them the cool place and let them dry out....more let them dry up until mid February when they can be brought out and promoted back to their old self.

Keeping them going as they have been by placing them in a good sunny window, cutting them back as needed, watering only as they need it and no fertilizing.
This method can encourage a geranium to keep going as long as the sun values desire them to. Soon though, they will lose their vigor and you can then either choose to keep them going strictly as a foliage plant....or put them into winter storage...

Winter storage is by placing them into a cool environment...cool....not cold...cool not warm.
A temperature range of 40 to 50 F can keep them until its time to re-invigorate them in mid February.
No water, no light, no heat should they touch.
No sprinkling....that could initiate mildew and rot.
Just let them go very dry.

The crawl space may be OK....if it has an earthen floor...dampness is probably prevalent So this would not be an ideal place. But, given a cardboard box...sitting on a heavy plastic sheet--should keep such plant in a dry state.
A bed of dry peat moss or dry sand could help ward off any moisture.
A room of the basement that is not heated...but not cold...
could also keep your geraniums over winter.

The other method is to use the plant strictly as a parent to many cuttings.