First off, how can you even get into/out of a Civic? Just about every cat I have ever owned has been higher off the ground than a Civic, so there isn’t much problem finding something taller.
Amongst the highest of the smaller cars were the older VW Golfs, and being hatchbacks they also have a fair amount of cargo space for their size. I’m not sure about the newer ones, but my 6’9” buddy managed to ride in the front passengers seat fairly comfortably. My Golf was also the only car I ever owned that my father-in-law with his bad back and worse knees could get into/out of without assistance.
Otherwise, you are pretty much looking at small SUVs, and of those, I have to say that the Element may be best if for no reason other than the way the doors and rear area are designed. Note that neither the Terrain nor the Jimmy (which the Terrain evolved from) qualify as “small”, and that the Terrain is only available with a 6-speed automatic. I’m not sure that the 4-speed manual is an option for ‘95-newer Jimmy’s either; they may also be slushbox-only. If you do decide to go mid-sized, expect 20 MPG or less ;)