Route Planning

There's a lot more options than just Google and Apple Maps, and they all have different benefits. Note that I don't drive, so these are all based around walking, cycling or public transport

Android Apps

• OsmAnd~ uses OpenStreetMap data and its own routing algorithms. It doesn't know about hills, so will give you some horrible routes for cycling. But it's all offline so works anywhere. The F-Droid version gives you free maps, the Google Play version charges you for maps, pick whichever you can afford.
• Citymapper is mostly for routing via public transport. But sometimes they make the most useful features paid-only, and some of those features only work in London. And you'll probably need an ad blocker

Websites

• OpenStreetMap is good for getting to know an area, with the cycle maps and public transport maps being a nice add-on. The various routing algorithms can sometimes give weird routes, and not in a good way
• TracesMap lets you quickly switch between Google Maps and OpenStreetMap views of the same map. Useful for comparing the two to make sure that the bridge you're relying on actually exists
• Trail Router has a routing algorithm that "prefers paths that go through parks, forests or by water, and avoids busy roads wherever possible." It can also give you an x mile round trip from any given point with the most greenery possible
• cycle travel is for bicycle journey planning. It doesn't know about hills for route planning, but will show them after planning a route. It is fairly decent at prioritising cycle routes
• traintimes.org.uk gives simple train times, especially if you're comfortable editing the URL
• bustimes.org is quite different to the traintimes equivalent, but is good for seeing what buses stop at a given stop (especially if you know the naptan code) and has live bus tracking for some buses. It's very manual work for anything other than looking up a single route
• Realtime Trains tells you exactly where your train is and what other trains are leaving or passing through the station soon. Less useful for routing, but very useful for knowing what type of train is coming, whether it's on-time, what platform, etc as well as what time you are actually likely to arrive into your destination
• gpx.studio is useful for when you know exactly what route you want to take and just want to turn that into a GPX file. Click along the route you want to take and it will follow paths and roads, making it quick to build the exact route you want to take before exporting to another app/site
• uMap lets you share the routes you've created with gpx.studio nicely
• Strava Global Heatmap shows what routes other people bike/hike/ski often. It's useful for deciding whether a route is actually good for cycling and finding popular running paths
• National Library of Scotland maps are great for historical context. Terrible for route planning, but good for answering "what used to be here"
• OpenRailwayMap for mapping railway infrastucture, past and present. It has limited use for actual route planning, but is good for answering "where does that train line go to?"