Hello! It sounds like you're planning an exciting trip to Hungary. Here are some tips to help you during your visit.

Best Time to Visit:
The best time to visit Hungary is during the spring (April to June) and the autumn (September to November). These periods offer moderate temperatures and fewer tourists. However, if you are visiting for specific events or festivals, the timing can vary.

Route and Accessibility:
Flights connect to Budapest, the capital city of Hungary from all major international airports. From Budapest, you can reach Aggtelek by bus which is approximately a 2.5-3 hour journey. Moving further, Miskolc is about an hour's drive from Aggtelek, and then from Miskolc to Szeged is a further 2.5-3 hour drive.

Accommodation and Booking:
All three destinations have a range of accommodation options including hotels, guesthouses, and bed and breakfasts. It is advisable to book in advance, especially during peak tourist seasons or during local festivals.

Clothing and Essentials:
Weather can be changeable, so pack layered clothing. Don't forget to pack a good pair of walking shoes, a hat, sunscreen and an umbrella. Also, it's always a good idea to have a map or guidebook handy.

Health and Safety:
Hungary is generally safe and has a good standard of healthcare. It's advisable to have a health insurance cover. Always carry any required prescriptions with you. Tap water is safe to drink in Hungary.

Local Etiquette and Respect:
Hungarians appreciate politeness and respect for their culture. In public places, avoid loud and boisterous behavior. Try to learn a few phrases in Hungarian - it would be appreciated by the locals.