Welcome to the Happiness Capital of Taiwan. Hsinchu is rated the happiest city in Taiwan, and Taiwan - the happiest country in Asia. You’ll emerge yourself in total joy and happiness here.
Now jokes aside. Hsinchu is one of the most BORING places in Taiwan. There are two main groups of people - engineers, and students, who want to become engineers. Nightlife - virtually non-existent. Night markets are in “OK” category, its lower end. Your ONLY escape from this happy place is regular and cheap buses to Taipei. You can buy 40 one-way tickets for 4000 NTD (100 NTD per ticket), or use your student card (105 NTD per ticket).
Rent of a decent “taofang” (small room with bathroom, usually no kitchen) is about 6000-9000 NTD depending on location. For new houses rent will be bigger, international students from Germany, for example, usually rent a flat in a new house (kitchen, several rooms, garbage containers), each paying around 10000-12000 NTD. Biggest problem is that it’s difficult to rent for 6 months, contracts are usually 1 year minimum. Good option is to find some foreigners who are already renting and join them. If you want personal flat - may be a little bit difficult. You can always try to rent for 1 year, and then just give away your deposit (usually 2 month payment), or skip paying last two months, avoid your landlord, then disappear into the night, silently.
For 6 monthsit may be a good option to just stay in the dorm, but I’ve heard that for NCTU exchange students males are placed in another campus, closer to city center, and there’s a free bus to deliver them to the main one. Not sure about quality of those dorms, high probability it sucks.
Good parts about Hsinchu? Five big supermarkets (2 RT Marts, 2 A-Marts, COSTCO) plus CitySuper and JASON’s for import munchies, 17-km coastal bikeway is nice, you’re as close to Taipei as to Taichung - 1.2…2 hours to both of them. And city is not that cheap due to rich IT engineers from Science City.