I was wondering if it is worth a day trip out to Hollokö (perhaps combined with somewhere else). Moreover, what would be the best mode of transportation to get there from Budapest? Thanks.
Hollókő is "interesting" but I would only go if there were something going on in town or at the castle. there is a bus and it takes 2 hours or you could hire a driver for I would imagine something less than 150euro which would get you there in under 1.5 hours.
Depending on the time of the year and your interests good day trips are:
Szentendre. Take the train up (about 30 minutes) and the boat back (about 45 minutes). About a half day experience. Very enjoyable.
Lake Balaton. My favorite place on the lake is the village of Tihany. Its a 2 hour train ride followed by a short bus ride. Great Hungarian arts and crafts and outstanding old church steeped in history.
Vac. I haven't been there yet but some swear by it. Especially if you are into mummies. About 30 minutes by train.
Great overnights include
Gyor / Pannonhalma