Try to take the Tilting Train , theres several runs a day and thats one of the newest trains in Taiwan. Its a tze-chiang train but not all tze-chiang trains are tilting trains. So do buy ur ticket a day or two in advance both for going there as well as coming back. The journey is faster, bout 2 and a half hours each way. YOu could stay in the town of Hualian . There are plenty of hotels. Probably could get a nice room in a small hotel for 1600nt/nite or so?? Or you could stay in the Formosa Regent for something like 6000nt/nite? And theres another resort or two nearby that are really great as well but they also cost close to 5000 or more a nite.
Food? YOu could exercise your credit card as much or as little as you want. Its always easy to eat cheaply in Taiwan.
I cant remember if the tilting train was about 700nt each way to Hualian or 700 roundtrip but I am leaning towards 700nt round trip. Make a quick trip down to the Taipei main station and buy your ticket and you will know.
blog.taiwan-guide.org/2007/05/ta … w-running/
edit: I just noticed you said from Hsinchu. Well add in the cost of the HSR to and from Taipei Main station (whats that? bout 600nt roundtrip?). And you can buy the tilting train from TAipei Main station to and from Hualian at your local train station in Hsinchu. You could buy a tzechiang ticket from there that connects with the tilting train in taipei as well. Or perhaps (I understand they are running the tilting train on the west coast line as well) you could simply take the tilting train from hsinchu to hualian and back.
And in Hualian they have buses that run to and from TienHsiang inside the gorge. They dont cost a lot.