Pittsburgh to Italy via UK

I think either way will work. Whatever you do you want to at least book a multi-centre flight US-UK and Italy-US as one ticket. Whether you add the UK-Italy leg on as well or book it separately depends on pricing and the convenience of flight timings.

If you want to fly to Florence what I would very seriously consider is booking the BA flight from London City airport (LCY). LCY is by some distance the best London airport to transit through. It's close to the city centre, easily accessible by public transport and the cut-off time for passing through security if you have just carry on is just 20 minutes. The planes are small so you need to check the rules on carry on bags.

You should be able to book the whole trip Pittsburgh - London - Florence - Pittsburgh as one ticket with either AA or BA.

You need to get yourself an ETA to enter the UK (assuming you are a US citizen) and will also need to pass through the EES system entering Italy. You may also need an ETIAS to enter Schengen - it should be introduced this Autumn but is likely to be delayed.

If you are going straight home from Tuscany, I would book a multi-city flight so you fly into London and fly home from Florence/Rome, and then just separately book a low cost flight from London to an airport near where you need to be in Tuscany. Low cost flights from London to Florence aren't that common as it's a small airport- but you'll find low cost flights to Pisa which is nearby (not sure how close that is to where you need to be). And of course plenty of flights to Rome. Depending on where you are staying in London it's very straightforward to get to Gatwick, Luton, or Stansted. Low cost carriers don't operate from London City or Heathrow.

Cat makes good points but I would not automatically rule out LCY. Firstly if you look to put everything on one ticket you may well find options using LCY that are competitive with booking the long haul flights on one ticket and a separate UK to Italy flight. You are quite likely to get a routing through LCY if you request Florence as both airports have short runways so can only be served by smaller planes. So BA have their flights to Florence from LCY rather than using up precious landing slots for smaller planes at LHR.

Secondly, whilst there are no "low cost" airlines that use LCY it doesn't mean that you can't find keenly priced flights from there. Admittedly we use LCY often because we usually check bags and BA offer them for free so comparing with the likes of EasyJet and Ryanair becomes a lot closer. But for me, the bottom line is that LCY is so much better to use that I am willing to pay a bit more.

Finally Cat is right that if you stay in the west of the city LCY is a bit further to get to, but then I would recommend staying more centrally anyway.

Agree with John that LCY is worth a small premium to travel from - you get the best views of London as you land, and the passenger experience at the airport is superb. I am normally out and in a taxi/DLR in 15-20 minutes from landing