We need to have district borders explicitly written somewhere, very visible for editors and easy-to-point for any new contributor. Here is the division I propose -- I would especially welcome comments from the people who know Budapest really well:
Castle Hill is only limited to castle walls; everything outside castle walls is Buda
Margaret Island, Hajógyári-sziget Island and other islands on Danube (are there any other?) are part of Buda
river attractions on Danube that are not connected to either side: Buda also?
Here's what I would recommend to those considering to start splitting a city into districts (but not make a strict guideline):
don't start districtifying a city before it's too much content on the city (32k editor warning?)
don't create first separate article for a district before you have enough content for it
to breed content for a district, start with separating that district in the city article listings--See, Do, Eat, Sleep
once you have a separate district article, there'll be many misplacements, and therefore questions "which district does this belong to?"; the more district articles you have, the more misplacements (and duplication) will be. Therefore:
find someone who can act a docent for the city (you?), once you have enough content for creating a district article
ideally ensure someone (you?) will watch over the city article and its districts for at least a year, fixing misplacements and removing duplication--otherwise, the districts (and the city article) will soon become a mess, much more terrible than before districtifying.
post on top of city's talk page a clear borders between the districts, and link to it from every district article's talk page--to reduce misplacements.
But by any measures, don't start separating content into districts if it won't help reader.