I wonder whether Bologna might appeal:
- Lots of historic buildings and cultural history, albeit not much in the way of Roman stuff from memory (though IIRC there is however an odd section in a department store where a Roman excavation is on display)
- Very walkable, with little in the way of hills, plus extensive porticoed pavements in case the weather turns foul.
- Only moderate amount of tourism. It remains a functional city
- Decent tourist office in Piazza Maggiore (aka Piazza Nettuno) who can help unearth some specifics
- The food is good!
Also worth a look is Aosta in Valle d'Aosta, with strong Roman roots, and a different (French Savoy) influenced twist on Italy. Getting there would require getting a train from Torino (but perhaps there are Milano connections as well?)
Another thought is Puglia (with a side trip to Matera). This very much would benefit from having a car, but many of the towns make for an interesting stroll around, and there's varied history from the Octagonal castle (Castel del Monte), through Venetian architecture in Trani, traditional stone 'Trulli' houses centred on Alberobello, all the way down to Gothic architecture in Lecce.
As Torino was mentioned, it certainly has lots of history, albeit much more Napoleonic / founding of the Italian nation, than Roman (there's a little, but not much). Quirky highlights might be walking over a bridge Napoleon commissioned, visiting underground (Museo Pietro Micca has you guided along counter-mining tunnels from a French siege, but I think there's also a different underground tour now), historic cafes that may have been the scene of plotting the reunification, scenes from the Italian Job movie, a fake (but reasonably convincing) mockup of a medieval village (Borgo mediavale), fancy buildings around Piazza Castello, hunting estate / country piles outside the city.
Whilst we're in that region, Alba in October is buzzing at weekends (and there's stuff on during the week) for the annual truffle festival. That's grown to become something of a food festival, with a most amazing outdoor market that rivals the indoor one for quality. It's not big, but is very pleasant and historic to stroll around (but gets a bit bustly on the Saturdays when the truffle fair is on). The events are well worth seeking out, from a sarcastic donkey race, mocking Asti's palio, through the medieval market and flag throwing procession, to arts etc.