I’ll start on a positive - that time of year can be a superb time to go. Weather often very good, but warm rather than hot, and that’s great if you’re actively visiting places. In addition, it can be superb for food, with good porcini & other mushrooms (finferli also good for instance), leading into white truffle season (which might lead you to extend the Langhe section if it’s late enough you plan to be there.
The rest may come across as being critical of your initial thoughts, and I’m sorry for that. We’ve spent countless holidays in Italy and very much have grown to love it. Away from the mass tourist trail we’ve encountered incredible hospitality, but the times we’ve ventured close to mass tourism, we’ve seen how that corrupts the attitude in locals (making it anything but the ‘real Italy’). We’ve also seen people disappointed by trying to cram too many tourist sights in, rather than really enjoying the places they visit.
Too many locations for 10 days - this isn’t one of those organised tours where you are bussed to their pre-determined view of what’s ‘best’ (most touristy) in Italy, but your planned holiday, with you handling the logistics.
For starters I’d say ditch Venice. It’s out of the way of your other locations, it being in the north-east, whilst your other locations are north west. Whilst it’s famous, it is blighted by tourism, and unless you carefully plot routes away from the mass tourist trail, can be a huge disappointment.
Cinque Terre can be lovely, but it too has suffered tourist blight, ironically as a direct result of Rick Steves trying to tempt US tourists away from the ‘big 3’ of Rome, Venice & Florence. The conveyor belt feel of English speaking tourists on the coastal paths (typically saying ‘buongiorno’ to each other, despite looking obviously like English speaking tourists) is not the experience it would have been before such exposure. The villages remain interesting (for now) and it’s easy enough to escape the crowds, plus the efforts at recycling and wider conservation by the locals are superb. Personally I’d drop this for some wonderful walks through the vineyards of the Langhe, almost all ‘free to roam’ due to splintered inheritance resulting in the need to have open access to the small parcels of land. The tourist office in Alba (Langhe, Roero and Monferrato tourist office) is exceptionally good, and their website also good, including for booking accommodation and winery visits. They have a superb cheap walking map (probably ~€15 these days) that makes planning walks through the vineyards simple.
Milan. If fashion appeals, then it’s an option, and one with choices of arrival airport and good transport links. If fashion isn’t a reason to go, then I personally found it disappointing, rather superficial and aloof.
Florence. It may make sense to have one of the ‘big 3’ tourist locations, and Florence has much you can see on foot. Lucca could be a day trip, or indeed the base, and if later in Autumn, San Miniato has a truffle festival (not as enjoyable or big as the one in Alba, but worth a visit if nearby). Lucca is a lovely small walled city, great to explore even on a wet day, and also has the superb Enoteca Vanni, with it’s back room cellar of older wines.
So my suggestion would be splitting the 10 days over just 2 bases, one in the Langhe, the other in / near Florence or Lucca. There will be plenty to see and do there, and the time you save not incessantly packing/unpacking, checking in/out, and travelling between bases, will be time that gets more productively spent enjoying your holiday. Look for either flights in/out of Pisa, or into Milan Malpensa and out of Florence (or vice-versa). You’ll want a hire car for the Langhe, but that may not be desirable for Florence/Lucca, but can be made to work if you find a nice place in the countryside that gives you options to easily drive to a car park in Florence etc. or even more ideally, be on a local bus / coach (aka pullman) route into the city, with the added appeal that buses usually drop you right in the centre, unlike the trains for much of Tuscany. Driving in the Langhe is enjoyable.
I hope this helps