I use a number of apps when travelling.
Agoda - This has been my go-to method of finding accommodation in the places I travel to. You can filter by price and rating, and they offer a broad range of places. Note that they do charge a small fee on to the price displayed. It works well, but the option to remember my card never works so I have to constantly keep putting it in.
Foursquare - Foursquare is something I heard about years ago and thought it was long gone. It's actually really useful for finding cafes or restaurants. People post tips and you can filter by places with WiFi or that are open now. Combined with Google Maps and HappyCow, I can easily find places to work and eat.
HappyCow - I'm not a vegetarian or vegan but I like to eat rice meals. I often find the veggie places offer huge plates of rice with vegetables, which suits me well. The app is a bit limited, as they try to upsell you to their paid version, but I've found some great places through it.
Google Maps - Before I travel somewhere, I grab an offline copy of the map for the area. I usually get a local SIM card, so I can browse live but it's good for when my reception is bad or when I initially don't have a SIM.
NewPipe - This is a YouTube client alternative that allows you to download video/audio, play in the background, or play in a pop-up window. I use it to grab videos or songs for listening to when on the move.
Photos - Combined with the Camera app on my phone, I use the Photos app to store screenshots or receipts for archiving. The photos sync online so I don't need to worry about them disappearing.
Podcast Player - I listen to a number of podcasts and this is the current app I'm using. Unless you buy the paid version then a bunch of adverts are shown, but this app is probably the best I've found so far.
Google Translate - The usefulness of this depends on the language of the country you're in. For places that use the Latin alphabet, where you can easily type it in, it's great. For places like Thailand, you have no change. I mainly use it to translate single words that I need, like Hello and Thank You. You can download the dictionaries offline for when you're stuck without internet.