Absolutely! Budapest, Eger, and Pécs are some of the most popular destinations in Hungary, and each has its unique charm. Here are some travel tips for your visit:

Best Time to Visit:
The best time to visit Hungary is during spring (March to May) and fall (September to November) when the weather is most pleasant. Summer (June to August) is also a good time, but it can get a bit crowded with tourists.

Route and Accessibility:
Your journey can start in Budapest, which is accessible by flight from most major cities in the world. From Budapest, there are direct trains to both Eger and Pécs. The total journey would likely be Budapest -> Eger -> Pécs

Altitude and Acclimatization:
Hungary's cities are at low altitudes so acclimatization isn't usually an issue. But if you have health issues, consult with your doctor before the journey.

Accommodation and Booking:
Hotels, guest houses and homestays are readily available in these cities. However, it's recommended to book your accommodation well in advance, especially if you are travelling during the peak tourist season.

Clothing and Essentials:
Pack clothes according to the season of your visit. Summers can be hot, so light, breathable clothing is advisable. Carry a good pair of walking shoes, as there is a lot of walking involved in exploring these cities. Also, packing a travel adapter might be helpful as Hungary has its specific plug type, F.

Health and Safety:
Ensure that you have comprehensive travel insurance before your trip. While Hungary is generally safe, it's always expedient to maintain general travel safety standards.

Local Etiquette and Respect:
Hungarians appreciate courtesy and polite behavior. As a visitor, respect the local customs and traditions. Dress respectfully, particularly when visiting religious sites or attending events or festivals. Keep in mind that Hungary's official language is Hungarian, learning a few basic words or phrases is appreciated.