This question taps into a rather broad array of misconceptions, out of date information, prejudices, and matters that lie at the boundary between snobbery and taste...not on the OP's part of course, who is simply being prudent, but on the part of the muddle of sources out there casually disbursing well-intentioned disinformation...
How to sort it out?
Well start by saying that while your hotel's address may be in the VIIIth, if it is at the corner of Rakoczi and Luther, two of those corners are ion the VIIth (the district that is home to the Opera, the Operetta Theatre, Andrassy ut, Liszt Ferenc ter, many embassies, and onb and on ... And your hotel is a good bit closer to the center of the VIIth than that of the VIIth.
Continue by noting that bobandco, like most everyone, has spent a good deal more time in the VIIIth than perhaps he thinks he has. The National Museum is in the VIIIth, as is the 'Palota District' just behind it, where the wealthiest middle-class Hungarians built their mansions in the late 19th Century, as their counterparts did on Fifth Avenue in Manhattan. Those mansions are still there (one is now the Budapest Public Library, another is owned by Magyar Radio, another by the Italian Institute) ... the district is referred to as the Inner Eighth" and has always been grand and continues to be.
The Outer Eighth is the area that most locals remain deeply prejudiced against, andy there was a time when aspects of that prejudice were justified (the part about prostitution; probably also pickpockets in the sense that many of them went home to the 8th after quitting work in the 6th, 7th, and 5th; neither of these is characteristic of the Outer 8th these days, in part because largest urban renewal project in Europe took place there over the past half dozen years, inn part because all of Budapest is rather safe, if not all beautiful these days, and pickpockets and prostitutes stay in the upmarket tourist districts to the extent they are around at all.
The Outer Eighth was a large swamp in the 19th Century, and festered with typhus, and was the neighborhood in which the very poor lived, the Jews and Roma and the unskilled day laborers who were brought in to build the city. So it was very poor and relatively lawless, but we're talking more than a century ago. It evolved into a poor district still, and remains so in chunks (much of the '56 revolution was fought door to door in the streets of the 8th) and it is still the Roma district as bobandco suggests, which is the reason why it is still bad-mouthed by many locals as anti-Roma prejudice is both unfounded and deeply embedded.
So, in sum, you are staying more in the VIIth than the VIIIth, a substantial part of the VIIth is among the most upscale areas of the city, and the remainder is no longer the sort of Dickensian swamp that it perhaps was twenty years ago.