Folks; some final confirmation on this question: the answer being YES, evidently MT and his wife & daughters did spend at least several hours in the territory now called Slovakia. I'm sure you are all just as relieved to learn this as I am.
The train that took them from Vienna to Budapest in late March of 1898 passed through Bratislava (then called Pressburg/ Pozsony) as well as other towns now part of Slovakia. It proceeded to the famous "Danube bend" at Visegrad, now a border town; and onward to Budapest. All of it was part of the Habsburg empire, of course. The story of the visit to Hungary is in Carl Dolmetsch, "Our Famous Guest" pp. 51-59.
Indeed it is the very train line that I rode on for our visit to Budapest back in March! And perhaps many others on here have ridden in the past... Small world.
Dr. Hal Bush
Director of the Undergraduate Program &
Professor of English
Saint Louis University
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314-977-3616
http://halbush.com
author website: halbush.com