There are a couple of places in the world where you could visit four capitals of different countries in 10 days with reasonable time for exploring each and one of those is touching the western Slavic area of what was once Czechoslovakia. It helps to have a car, although you could probably train it.
After BP, you could head to Prague, the capital of the Czech Republic, about five hours away, with a several-hour stop in route exploring Bratislava. In comparison to the other capitals, Bratislava, Slovakia, is by far the smallest, making the trip to Prague an easy one-day journey.
Following a few days consuming paprika-laced grilled sausages, roasted pigs knuckles, and tasty frothy beers in Prague, you could zip down to Vienna, the capital of Austria, only a 3.5-hour drive, to round out the tour.
It’s a relatively tight circle. And although all four countries are part of the EU, you’ll need three different currencies as Hungry, and the Czech Republic have resisted submitting to the euro.
However you might “do” the trip, it’s worth the investment of 10 days just for the food and drink. Throw in the impressive architecture, the walking culture of each city, and easygoingness of the local inhabitants, and it makes for a sensory-filled, non-stop, yet relaxing and memorable excursion.