less than 100 miles SW of Budapest, reachable through South Station. My dad and I got on a train, and got off at the small but pretty town of Balatonfured (Balaton Hot Springs), had a delicious lunch at the dining room in the Hotel Uni ($23 with tip for two people having a full course meal including a fabulous bottle of local chardonnay), and walked around the town and enjoyed the quiet and the total absence of English speaking tourists. There are other places to go, like Siofok (across the lake from where we were).

Although we did not go there, another town which was recommended to us was Esztergom, the cathedral city of Hungary (the famous Cardinal Mindszenty was actually the Archbishop of Esztergom).

Enjoy.