As other big cities, Budapest also has its areas where taking your camera out of your bag may mean a threat to the security of your valuable equipment.
I highly doubt you'll ever visith the 8th district, not Múzeum körút and its surrounding area, but the area close to Nagykörút, where tram no. 4-6 runs (next to stops: Corvin Negyed, Harminckettesek tere). Be sure to walk streetwise in order to avoid unpleasant situations.
However, it's more likely that you'll find yourself taking a stroll near Blaha Lujza tér, Wesselényi utca, Király utca. The main road itself is relatively safe (Nagykörút); however, Akácfa utca and Király utca may not be the best place to take photos after sunset, despite of the fact there are usually many people around at that time as well.
The group of considerably unsafe areas also include certain parts of Újpest, Kispest, Kőbánya-Kispest. Avoid these areas and you will be doing fine during your stay. Of course, buses are also home to pickpockets, just like in any other big city, but if you hold on firmly to your belongings, no harm will come to you.
If you have questions concerning your personal safety and stay in Budapest, feel free to leave comments below.