We stayed at the Pilvax Hotel a few years ago and found it very attractive.
It is within a few minutes walk of Vaci Street, the pedestrian mall with a
lot of shops and restaurants, and is also well located for other sites of
interest in Budapest. I recall that it was very reasonable at the time. Just
to make sure, I pulled up their website and found that, for August, their
rates are about US$75 for a double room. I believe breakfast is included in
that rate. You might want to check this out by going to their website:
The only downside we found was that there was no elevator. Hope this helps.
Howard in Vancouver