I would highly recommend you go to Taroko Gorge....it is stunning. If you're on a budget you can take the train to the closest town and then the hop on hop off bus. The best way is to negotiate a car service to either pick you up at the train station closest to the park or to simply negotiate a car service directly from your hotel in Taipei.

The car service guys do this trip all the time and know exactly where to bring you so you see all the main sights. 4-6 hours or so at the gorge with a private car is enough time to take a few 1-2 mile hikes and see some of the major attractions. We booked a private driver from the local train station for a little over $100 it was well worth it. I had gotten a quote for $130 for a private car tour direct from our Taipei hotel.... if I had to do it again I would have booked the driver direct from the hotel (door to door) and skipped the train option. However if the bus and or train is the only option within your budget...do it.

If I understand it correctly you're going with a few elderly folks so a private car would be your best option. English speaking driver, Comfort, convenience and air conditioning...need I say more.

Also, if you're so inclined the driver can drop you off to jaunt down a trail for as long as you like and can chauffeur the older folks to view other sites while you stretch you legs and venture down the trail for a bit.