Today I discovered Rome2Rio, which is a multi-modal travel search engine. I've been looking for such a tool for some time. Instead of searching only flights, it provides train and bus routes, and allows to mix and match all of these (and even ridesharing) to find the best way to go where you want. It also features door-to-door pricing, which means not just the cost of the flight, but also any shuttle you may need to use from the airport to city center.
They have their own dataset and don't do API queries to other operators. There is a risk of out of date data, but on the other hand, this makes the search super-fast. The trip is visualized on a map and you can easily see what's the best solution.
I can finally plan mixed train/bus/plane trips easily!