From the US, there are really two options:

Fly into Birmingham UK

For my money, this is the easiest. Small airport, quick and easy arrival, security and customs. Uber from here to the hotel is about $50 - make sure you get one big enough for all your bags!

Downside - there's a layover in Europe, either Paris or Amsterdam. That makes the trip a little longer.

Fly into London-Heathrow

This is everything Birmingham isn't. It's big, bustling and bloody annoying. It'll take longer to get through the airport and you're still a little ways from the Hotel. The upside is you can get a direct flight from the US.

Options from Heathrow

Uber - approx $200 for a regular Uber but a larger one will set you back up to $400. Taxi will be a similar price.

Train - there is no direct route to Straford upon Avon by train. Check out:

https://www.thetrainline.com/journey-planner or

https://www.goodjourney.org.uk/journey-planner/

for some helpful route ideas.

Bus - buses to Stratford upon Avon leave regularly from Victoria Coach Station (https://www.nationalexpress.com/en/help/coach-stations/london-victoria)