I think you are on the right track, but won't be able to do everything on your list in one day. It will be too late to do much when you arrive: but you can have a nice dinner in town *before* heading to the Holiday Inn. On Saturday, I would leave all luggage at the Holiday Inn.

--1st head to the NPM first thing--with travel, tour, and many exhibits, it's at least a half-day proposition. You might have lunch there (or head back to town, but museums make me hungry).

--Then CKS Memorial (and surrounding park). If you're feeling ambitious, you can then go to the Eslite bookstore in the Eastern District (not the original one)--which puts you by 101, if you still want to do 101.

--toward evening, Longshan Temple. That then puts you by a very nice night market for dinner/snacks, and you don't have to go out to Shilin. You could, after Longshan, head to the Yongkang Street area for dinner (now all accessible by subway). Then finally pick up your luggage and head to the airport hotel (not a bad idea for an early flight regardless of financial considerations.

Tea: many outlets everywhere, including if I remember rightly Tian Ren shops opposite the CKS memorial and also in 101. There's also the PageOne bookstore in 101. If you are into temples, Baoan and Confucius--and also Xingtiangong--are well worth visiting, but you don't have enough time unless you skip other things.

Din Tai Fung: I like it fine, but it's nothing that special. No need to make a point of it, especially if you have to queue up for it. Lot's of other & more interesting food options. Look around; as noted above, I would eat on Yongkang St. at least once--a possibility for lunch if you're done with the museum in time. Betel nuts: a very mild rush; bitter taste takes some getting used to; causes throat cancer.