This will take a bit of research on your part to determine the full list. At a minimum you will need a GPS mapping tool for local trips to see what transportation systems you will be riding. Then internet access determine how to get tickets (whether you need the app or can just purchase them directly by using a credit card or your phone. Here is a list of suggestions that may be useful:

• Airlines app – this is a must have app. You will need this to get updates on your flight, particularly gate changes.
• Toilet app – You won’t miss this app until you need to go.
• GPS mapping app – this is the most critical time and budget saving app to have.
• Translation app with the ability to use a camera to read labels
• Train station locker app – optional depending on whether you need to check in to your hotel early and your hotel doesn’t offer this service.
• Train and bus apps – may be necessary for buying tickets. 
• Ride-share – download the app you expect to use prior to leaving home.