If I understand the question correctly, you're looking for hotels near the relevant stations in Paris and Turin.
In Paris you will need the Gare de Lyon for trains to Italy. There are a lot of hotels in the area: I have used the Hotel Corail, which is fine on a budget. GdL itself is about the size of London Victoria, and like Victoria in two parts, 'blue' and 'yellow', iirc. One section has numbered platforms, the other lettered. The last time I did the trip the train left from the lettered portion.
(The train itself helpfilly has 'Paris-Lyon-Turin-Milan' painted on one side, and 'Milano-Torino-Lion-Parigi' on the other, but does run as half a double unit for part of the journey.)
For Turin to Milan, look for somewhere near Porta Susa station rather than Porta Nuova. PS is a smaller, modern through station built for the high speed line, and easier to navigate. There are hotels nearby (I have one booked for November).
All that being said, Turin to Rome is a long way for a day trip. Milan and Genoa are both well worth a visit, and much closer.
Cheers
Yes I found a hotel near the station in Turin so I was hoping to do the trip over 5 days with two stops in Paris. I’m travelling from Edinburgh so im use to the 4 hour journey I don’t know how tiring it would be. My plan would be
Day 1: Edinburgh to London and catch the Eurostar to Paris (I do this trip in October anyway and regularly do it to Brussels)
Day 2: Paris to Turin dropping my suitcases off and heading to Milan for a few hours
Day 3: A long trip to Rome but I could still be there 11am to 7pm and see many sights ?
Day 4: Turin to Paris so another 5 hour leg arrive in Paris at 1.20pm but I can relax and get some lunch catch a late Eurostar back. Stay in London at Kings cross for the evening so it’s only another 2 hours travel that evening.
Day 5: Edinburgh to London
I can add an extra night in if need be but I rarely go away on holiday for more than 5 days and I don’t like flying much. It’s for a honeymoon so I have enough going on with the wedding.
My other opinion is scrap the Rome day out and stick to Turin and Milan as you say as that’s less tiring. However I was particularly keen on Rome due to it being more touristy. I’m not sure what there is to see in Milan other than a couple of sights.
It’s obviously long train journeys but back in January I did Brussels stay over and visited Amsterdam, Cologne and Bruges for a day but these were 2 hour journeys at most where as that’s Rome journey takes much longer, it’s quicker from Milan but I wanted to avoid that 7 hour train journey.
The scenery in the french alps looks great if I do go by train it just boils down to how tiring it would be.