It proved very easy to do Kekes (1014m) as a day trip from Budapest. The highest hill in Hungary is according to Wikipedia the third most popular tourist attraction in this country, after Lake Balaton and the Danube.
There are at least three direct buses daily (Volanbusz) from the Stadium Terminal in Budapest to Kekesteto Sanatorium, a distance of approx 100 kilometres. I took a bus that left at 9:15 am, paid 1860 forints (equivalent to 8.50 USD) in the ticket booth, and arrived Kekesteto at 11:15 am.
From the sanatorium it is only a few minutes walking to the highest point, which is marked by a stone, painted in the same colours as the national flag (red, white and green). The true highest point is actually behind a fence just a few meters away. But this is probably a man-made hill, an overgrown concrete foundation where the old antenna/tower once stood.
I also took the elevator up the new tower, which cost 480 forints. It was much better view from here, since the summit of Kekes is covered by dense forest. I had an hour or so to roam around the summit, before I took the next bus back to Budapest at 12:35 pm. This is probably my easiest country highpoint achieved so far! Hence no achievement at all.
Back in Budapest I did a lot of sightseeing and walking, to compensate for the very short walk on Kekes. Budapest really surprised me, this is maybe the most beautiful city I've visited in Europe. The nightlife is awesome too, there are plenty of outdoor restaurants, bars and music venues.
Kekes at EveryTrail