155/80 R13 would be a narrower, lighter weight tire that is about the same height as the 175/70 R13 and the CRX is well within the weight range of the 155mm wide tires.
Another option is going up to 14" rims (off a older civic hybrid, civic hx, Honda insight, or any number of other vehicles) and getting 165/60 R14 tires and getting low rolling resistance tires as well, at least that is what my plan is as the Civic VX calls for the same 165/70 R13 tires as the CRX and they are getting hard to find.
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