That seems like a lot to try and pack in. I seem to recall it taking a few hours each way between Taipei and Taroko plus time to explore there would be a full day on its own. To add a night tour on that evening seems like too much to expect to me. Especially if you expect to do a full city tour the next day.

Frankly I would just do a little research on things that sound interesting for Sunday and see them on your own. You could spend all day at the National Palace Museum alone. Or at least a few hours anyway and it tends to be quite crowded with bus tour groups from the Mainland. Things like CSK Memorial Hall are very easy to reach on your own. The "handcraft center" sounds like a tourist trap designed to sell you things. There are several traditional temples around the city. The Confucius Temple and Baoan Temple are very near to one another (a couple of minutes on foot). Taipei is generally easy to get around and the MRT goes most places you want to go or gets you pretty close. The main exception being the National Palace Museum which requires a bus after you get off the train. So a taxi might be a better option if you're pressed for time.

You basically have only a day and a half. As much as I liked Taroko Gorge, you're probably better off just touring Taipei. Also depending where you're coming from, don't forget to factor in jetlag if applicable.

Elephant Mountain is a good climb if you're up for it. The city at night from up there is a pretty awesome sight.