Subject: Hungary Question

I will be traveling to Hungary in June. I am interested in visiting the following places outside of Budapest. My first question is whether it is possible/advisable to try to see Szentendre, Visegrad, and Esztergom in one day. I would be using public transportation. If only one or two were possible, which is most advisable to see?

Also, has anyone been to Godollo and the palace there? Worth a detour?

Any other comments about Hungary and Budapest would be appreciated. This will be my first visit there.