Yes. Since you are traveling by private transfer rather than a fixed train or bus schedule, you can add a stop in a nearby town like Eger or a stretch of the Bukk hills on the way to or from Miskolc. Your route and timing are built around what you want to see, not a set timetable.
Miskolc is roughly 180 km (112 miles) from Budapest. A private transfer covers this in about 2 to 2.5 hours, dropping you directly at Lillafured or the Cave Bath rather than at a train station in central Miskolc. That matters here because Lillafured itself sits a further 8 km (5 miles) outside the city center, so travelers relying on trains typically still need a taxi or local bus to complete the trip.
Most travelers spend a couple of hours strolling the hanging gardens, exploring the palace grounds, and taking in the lake and waterfall views. Add another two to three hours for the Cave Bath, since the pools and passages are worth lingering in rather than rushing through. A full day trip gives you a relaxed pace for both without feeling like a checklist.
The hanging gardens are the highlight, with terraced paths that make for an easy, scenic walk around the palace. Nearby Lake Hamori and a cascading waterfall add to the setting, and several caves in the surrounding Bukk hills, including Szent Istvan Cave, are open for those who want to extend the visit. It is a compact area, so you can see the key sights without a lot of walking between them.
The bath is built into a natural cave system that stretches over 4.8 km (3 miles), with connected indoor and outdoor basins fed by warm, mineral-rich water long valued for its recuperative qualities. You swim through passages lit and shaped by the rock itself, with a different feel around every bend, quite unlike a standard thermal pool. Bring swimwear and a towel; lockers are available on site.
Miskolc pairs two very different experiences in one trip. Lillafured Palace sits in a forested valley with terraced hanging gardens and lake views, giving you a peaceful, palace-in-the-woods atmosphere rarely found so close to a major city. A short drive away, the Cave Bath of Miskolctapolca lets you swim through natural cave passages shaped by thermal water over thousands of years, one of only a few bathing experiences of its kind in Europe. Nature, history, and a genuinely unusual swim in a single day.