Day trips out of Budapest - North or South?

Haven't been to Lake Balaton, but I was in Eger and Szentendre. You could easily do Szentendre on your own and you would only need half a day for it as it is small. However, this would only be if you run out of things to do in Budapest as it isn't that amazing to see. Eger is very nice and it is nice to get away from the big city and stroll around here.

We did Budapesting's Eger, Danube Bend and the Lake Balaton Tour as well and we can highly recommend it. The two of us had our own tour guide, he was very friendly. The Hungarian countryside is very beautiful and it's well worth getting out of Budapest to check it out. Hungarian wines are very celebrated within Hungary, and although they weren't up to French standards, it was great that the wineries pour generously (too generously perhaps!) and are much more friendly and relaxed than their western european counterparts. Be warned that there are never any spittoons and generally the staff at the cellar door are afronted and offended if you don't finish whatever they've poured for you to try (up to half a glass easily!) It took much explaining and eventually we shared a glass to minimise waste and offending them!

While the lake region (Balaton) may be a nice extended vacation for relaxation, I dont think the travel to/from Budapest for one day is worthwhile. It's a nice lake, but not awe inspiring. Eger is more enjoyable. Another thought, though, might be to take a tour of Kecskemet, it is a nice, typically Hungarian small town, and then see/visit the Hungarian plains (Pusztah) and take in the farm lifestyle. This is especially good with kids, as you can take hay rides etc into the fields. I believe there are tours from Budapest. If not kids you might want to consult with your guide to make sure there is enough things of interest.

The Danube Bend Tour gives a perfect and very compact overview of what the Hungarian countryside is like. Also that is the shortest day trip from Budapest.

I could (and have) easily spend four days just in Budapest. I wouldn't recommend Szentendre - I found it very touristy. I quite enjoyed a half-day trip on my own to Godollo. Eger is fine, but I would have thought it was a bit far for a day trip.