Szentendre is just a short ride from Budapest, so it's become popular as a side-trip when visiting the capital. Its laid-back Mediterranean flavor and photogenic streets make it worth a visit - but be prepared to share!
Szentendre has been inhabited since Roman times, and has been a center for populations of Serbians, Bulgarians, Croatians, Macedonians and Greeks. Its different waves of inhabitants have lent it a feel more Southern than Eastern Europe. Looking around at the Baroque architecture and cobblestone lanes, you could think you're in Croatia.
The town has a lively arts scene, as well as some fine museums. And, of course, there's everything a tourist would need - hotels, restaurants and bars all crowd for the service of the visitor.
If you want to see Szentendre with a bit more elbow room, time your visit away from weekends, particularly in summer, when it's peak tourism season. The town sits on the Danube Bank not far north of Budapest. You can get there on Highway 11 by both car and bicycle; otherwise, trains and buses leave regularly from Budapest and take about half an hour.