Can anyone who knows the city well recommend a good part to stay in? I will be travelling from Vienna by train and probably be using Airbnb for accommodation. I am in my mid-sixties, enjoy walking (using public transport where appropriate) and will be visiting some of the recommended attractions mentioned in other posts on Budapest. I would like to try some really good Hungarian food, I'm more a wine drinker than a beer lover and not interested in touristy nightlife attractions. A classical concert would appeal if it would be easy to return to my apartment/lodgings at night safely. I quite enjoy klezmer music but don't know if that is big in Budapest.
Any assistance will be greatly appreciated.