Some new cycling lanes on Alkotmány utca in District V are the best facilities that have been implemented in Budapest, perhaps showing the city is finally taking bicycles seriously as transport. The lanes are good for a number of reasons. First, they're on the street, rather than the sidewalk, and thus integrate cyclists with motor traffic, which, in an urban context, moves at roughly the same speed. Second, there's a separate lane on both sides of the street, allowing the cyclists to move in the same direction as other road users in adjacent lanes. This is in contrast to the shared-use paths that constitute most Budapest cycling facilities (as on nearby Bajcsy-Zsilinszky út) where a single, bidirectional track runs along only one side of the street).
The closest thing we've seen to this type of facility to date is Andrássy út. But the lanes on that street are flawed because they run down a narrow gap between parked cars and the sidewalk, putting cyclists in danger of getting "doored" by passengers exiting vehicles. Check out this video (Nine Reasons Why It's Great to Bicycle in Budapest). Reason No. 8 illustrates the problem nicely. (http://www.hirszerzo.hu/patroview.1.23)
The Alkotmány lanes are of a type referred to in some quarters as "share rows" because they can also be driven on by ("shared" with) motorists. It's a popular solution among many road departments because they provide accommodation for cyclists without taking space from motorists. Of course, Budapest City Hall has always feared the political backlash of taking space from motorists. But there's now an emerging, quickly growing constituency of city cyclists. So some compromise is needed. The NGO MKK (kerekparosklub.hu), which is partly funded by Budapest City Hall, successfully lobbied for share rows on a trial basis.
I have mixed feelings about share rows. I can understand that on very narrow streets, it's impossible to provide separate lanes for both motorists and cyclists. But when share rows are used out of simple political timidity, it is running the risk that motorists won't give the lanes any respect, at all. In the 1980s, the city of Paris installed share rows on a similar trial basis, and the experiment failed for this very reason. These days, Paris is building a combination of lanes as well as facilities that are separated with physical barriers such as curbs, posts and speed dots. Cyclists are now an accepted part of traffic there, but this can be credited, at least partly, to city's firm steps to stake out cycling territory.
Perhaps share rows will work better in Budapest. I say this because, in contrast to Paris in the 1980s, cyclists in Budapest have already insinuated themselves into traffic -- with virtually no help from the city. It's my feeling that if and when the city starts building decent infrastructure, cyclists will fill it up quickly and motorists won't be able to ignore them.