May is a super time of year to visit, with the cities (usually) not too hot, but enough warmth and daylight to explore the countryside and enjoy the colours it offers.
I'll echo
@BethC 's comment about must sees - very much a matter of personal tastes and I've learnt that many of the mainstream touted 'must sees' don't tally with what we want to see & do, whilst ours might seem utterly mundane to others wanting to see the famous sites.
As well as train & taxi / private driver, it's also useful (especially in Tuscany) to consider regional buses (the inter-city ones called 'pullman') and indeed organised trips e.g. via the tourist office. The bus network is good, and unlike the trains, will typically drop you in the centre.
I agree with you on smaller tours - and it can help that the quirkier stuff is naturally that way. If travelling solo, they can also be a way to ensure some socialising, with the ability to limit it to just that day, or arrange to meet again on another day with any people who you get on really well with.
I find Trenitalia an easy site to use, and booking in advance can save a lot of money (on already reasonably price trains). This makes trading up to 1st class on the fast 'freccia' trains a very affordable luxury, and such journeys have become a pleasure in their own right, not just a functional necessity.
For a month-long stay in one city, I'd be tempted to avoid the usual tourist focus of aiming to stay 'in the centre', but instead look for somewhere where you'll have a bit slower pace / surrounded by locals not tourists. This might mean a pleasant suburb, or somewhere a little further out, but with easy bus connection into the city (and/or close enough to get a taxi 'home'). Definitely an apartment for the flexibility / space it offers. By way of example, our 1st two visits to Bologna were day trips via train from further away, and that didn't work well for us, with my partner simply wanting to go back 'home' at lunchtime on the one trip. It got one last chance for us, with us staying south of Bologna (Rastignano), which was a 45 minute bus ride in, but crucially that bus journey ends at a very central location. We enjoyed every trip in, yet also enjoyed being out in the countryside. It worked well enough that we've returned to stay in Bologna itself a couple of times since. I reckon a 20-30 minute bus ride away is often ideal, to get into the countryside (or a nice leafy suburb), but where it feels easy to get into the city (and to get back out again).
A couple of easy day trip options to throw into the mix:
- Colle val d'Elsa, which had charm and a modest level of tourism, which struck a nice balance for us. Also it's a place known for glass-making if that appeals
- Lucca, which is a lovely manageable size for a day trip, unusually for tuscany has its train station just outside the walls, so very convenient, and has a lovely peaceful feel to it.