Mid - late October is typically a super time to visit if you want to be active. The weather often comfortable, even warm, but not hot. Rain surprisingly rare.
Flight arrival time usually influences our plans. If morning, we'll typically crack on to our 1st base, but if in the evening will have us considering either an overnight stop, or a stay of a few days in the arrival location. What we tend to avoid is a 2-3 night stay as that never feels enough to get settled. an overnighter conversely acts as brief respite, but barring a meal in the evening, we're not looking to do anything in that location, so it serves its purpose. So for Rome I'd say either crack on to Tuscany, or have an overnighter... or give it a few more days to give it a fair opportunity to impress.
In general 1st timers in Italy often try to cram too much in, staying only briefly in places before moving on, ending up not really experiencing a place properly, and having lots of hassle packing and unpacking, checking in and out, then travelling to the next destination, all the while feeling vaguely disorientated. I blame the glossy magazines / organised tours.
As a rule of thumb I'd suggest minimum 3-4 days stay per location, but for places like Rome or Florence where there's much you might want to see, having a full week is far from crazy. A day trip or two during that week can help widen horizons and we've tended to use such day trips as 'samplers', often leading to a return trip on another holiday, where the place gets a full 'base location' stay (e.g. Bologna, Trento, multiple places in Le Langhe). As such I liked your initial thoughts, but don't be afraid to have those day trips as 'options' rather than being inked into a schedule. Let your enjoyment drive what you do each day.
