How about Green Island?
I would assume the Bassman family has a vehicle, and from Taichung it's about a 5-6 hour drive to Taidong. From there it's a 13 minute hop by plane to Green Island. Flight costs 1064NT return, with the little Bassman flying for free. Can also be done by sea from the port of Fukang, about 20 minutes north of town on the Hua-Tong Rd. If you decide to go by ferry, I would recommend the Liu-dao tz-shing, which is the largest and safest of the Island plying vessels. Count on about an hour trip depending on sea conditions and be forwarned, it can be a rough ride especially this time of year.
The Island boasts stunning scenery, amazing indigo blue waters, a beach for the Spouse and little Bassman to play while you explore the underwater world, and finally one of only 2 seaside hot springs in the world. Scooter rentals are about 350NT a day, and it's easy to get around as there is only one road to speak of. Shopping is more availible now that Green Island is on the tourist rader.
A hotel will run you anywhere from 1,000NT to 3,000NT per night depending on your comfort level. If you are a scuba diver, some of the dive sites can truly be world class! Over the years I've seen sharks, a 9 foot moray eel, sea turtles, schools of barracuda and jacks, and fantastic coral formations.
On a final note, Green Island has a first class campground, nothing at all like the crap normally associated with camping here. Has running water, a very chill setting, and best of all space between the individual camp sites. Cost is 350 per night, providing someone is there to collect! It's also located within walking distance of both the hot spring and the beach.
Might be worth checking out..................................
Enjoy your holiday wherever you end up!