The buses and the metro in the city are regular and run throughout the day and night. I feel pretty safe on them even when they are overcrowded. The biggest issue I have is sometimes I will get on the wrong bus going the wrong direction. When that happens I have to get off, cross the street, and wait for the correct bus. It's like the saying of measure twice, cut once. Check the bus location twice, only get on one.
Mostly I walk. I like to get my steps in and it is easier to see the city and the amazing architecture. Especially as the weather has cooled off and the seasons have changed it is much nicer to walk and be outside. However I am sure once it gets colder I will gravitate towards the bus more.
To get to other areas in Hungary, I have to take the train. There are trains all over Europe and you can get to most places in Hungary in a few hours. My trip to Pécs took roughly 3 hours while my trip to the Lake Balaton area was under 2 hours. I like sitting and watching nature pass me by or working on my projects. It is very peaceful most of the time. In the smaller cities, the buses run less frequently, so I walk much more. This can get annoying especially when I decided to walk the 30 mintutes from the train station dragging my suitcase along. I should have just figured out the bus sooner! But what can I say... I'm stubborn.
My favorite place was Tihany, which is a peninsula on Lake Balaton. That means its an area surrounded on three sides by water, similar to Florida. Tihany is famous for its lavender fields and many stands were selling lavender products including soaps, perfumes, lemonade and even toys that smelled of lavender.