I'm glad to hear you're planning to visit Eger, Tokaj, and Pécs in Hungary! Here are some essential travel tips to consider.

Best Time to Visit:
The best time to visit these Hungarian cities is from April to October, where the climate is warm and there are many festivals to enjoy. However, if you're a wine lover, visiting Tokaj during the grape harvest season in September and October would be ideal.

Route and Accessibility:
Eger, Tokaj, and Pécs are relatively easily reachable from Budapest through the Hungarian InterCity trains. Alternatively, renting a car could give you flexibility to move around at your own pace.

Accommodation and Booking:
You'll have various accommodation choices ranging from budget-friendly to luxury. I recommend booking your accommodations in advance especially during the peak season to secure your place. Websites such as Booking.com, Airbnb, and even the Hungarian Tourism website can provide a wealth of options.

Clothing and Essentials:
Pack clothes according to the season. Don't forget your comfortable walking shoes, hats, sunglasses, and sunscreen for the warm months. Carry an umbrella or a raincoat if traveling during the rainy months. Essentials like a travel adapter, a basic first-aid kit, and maps of the cities could be handy.

Health and Safety:
Hungary is a relatively safe country but it's always good to have emergency numbers stored. Carry your health insurance card/details and if necessary, know the locations of hospitals in these cities. Public drinking water is safe to consume.

Local Etiquette and Respect:
Hungarians are typically polite and reserved. It's important to respect their customs and traditions. Church dress codes are strict, particularly for women. Learn a few basic Hungarian phrases as it's greatly appreciated.