Siena

Florence (airport code: FLR) is the closest airport.
Rome (airport code: FCO), which is a much larger hub, has a wider choice of flights, often a bit cheaper than flying to FLR, but is farther therefore the savings may be offset by the higher ground transportation costs (trains and buses).
Not knowing what your home airport is, I can only suggest to go to Kayak and check flight options to FLR or FCO and make a decision.
The train cost from FCO to Florence is about €60 (US$70), for about 2.5 hour trip, then you need to take a bus from Florence to Siena (another 75 min). Haven't checked the price now, but it's a bit less than €10.
If you fly to FLR, you need to take a shuttle bus or a taxi to the city center (€6 or €20 respectively), which is less than 20 min. away. Then take the same bus mentioned above to Siena.
If you fly to FLR you save over 2 hours and about €40-€55 in ground transportation costs.
There are cheaper options from Rome to Siena, such as a bus which departs from Rome Tiburtina station (Sena Bus Company). But it will take longer than the train.

I did that a few years ago. Flew into Rome and took a bus. That involved taking a train from Fiumicino to Rome Tiburtina station, which is adjacent to the bus that goes direct to Siena. It was a little confusing, but I figured it out okay and it worked out fine.

I would guess it's easier if you fly into Florence, but flights from the USA to Florence are going to be more limited than flights to Rome, depending on where you're coming from.

I did that last summer and flew into Milan and then trained down to Florence and train to Siena. Yes the bus is faster but it was at night since I spent the afternoon in Milan so I opted for the train the whole way.

I saved a few hundred dollars flying into Milan vs Rome from the USA. Florence and Pisa was more then both from my starting point. I looked at the price of each vs price of transportation from the airport to siena via trains there and to from airport to get a total figure. Then I made my choice. I didn't mind the couple hour train ride from Milan to Siena in the early evening so I opted for that vs my budget.

From the US I don't there are any direct flights to Florence and I suspect it will be always more expensive to fly into than Rome or Milan from the US
So although more convenient to reach Sienna ; your total travel time and cost is likely higher than sticking with one of the two bigger places and train within Italy.

If you were flying from some parts of Europe than it likely would be better to fly into Florence.

As I mentioned, the best strategy is to check flights from your own airport to either Florence or Rome and see the flight options and the price difference. A lot will depend on which airport is your home airport, therefore there is no magic answer.

For example my home airport is SFO. There are no direct flights from SFO to Italy, therefore I will need to stop somewhere first no matter what. It could be somewhere in the US or in Europe. I go to Florence every year (which is only 40 miles from Siena). In my case it is much faster (and ultimately cheaper) to take a non stop flight from SFO to Europe (FRA, CDG, MUC, ZRH) then from there connect to a flight Florence, than it is to fly to Rome and then take a train. In my experience, the airfare price difference between Rome or Florence has never been large enough to cover the extra train cost, therefore the only time I fly to Rome or Milan, is because I need to go there for other reasons. In all other cases I pay a bit more to fly to Florence, because I save time and money.

Your case might be different. If your home airport has no direct flights to Europe, then you will need to connect to a US hub (maybe New York or Washington or Chicago or Atlanta). In that case the Rome option might be best because all those cities have a direct connection to Rome, but none to Florence. Therefore in that case to fly to Florence you would need 2 stop-overs, which will definitely take longer than flying to Rome with one stop-over only and take the train from there.