Yes, travelling between Prague and Budapest is simple and convenient. The cities are about 530 km apart, and you can take a train, bus, or flight. Trains are a popular option, taking around 7 hours, and buses are slightly cheaper, with a journey time of 7-8 hours. Flights are quicker (about 1.5 hours), but train and bus journeys offer scenic views of the countryside. 

The best time to visit both cities is during the spring (April to June) and autumn (September to November) when the weather is pleasant, and the cities are not overcrowded with tourists. Summer (June to August) is also popular, but it can get crowded, especially in Prague. Winter (December to February) is ideal for those seeking festive Christmas markets and a quieter experience, though it can be quite cold.

Yes, both cities have efficient public transport systems. Prague has an extensive metro, tram, and bus network, making it easy to navigate the city. Budapest also has an excellent metro system, buses, and trams, as well as taxis and ride-sharing services. Both cities are walkable, especially their historic centers, so you can also explore on foot.