
The City of Budapest is doing what they can to improve safety and facilities for cyclists. The city enjoys a very respectable 4% modal share for bikes and there is a lot of focus on improving that and mainstreaming urban cycling. There are several stretches with bike lanes, like above.
All in all it's positive in Budapest. Loads of work to be done, including the classic task of convincing their politicians and Department of Transport of the necessity of constantly improving the infrastructure and mainstreaming bicycle culture.