Agree with Maoman. It’s easy to get to NTU from Mucha. By car it’s quick and by bus it’s not much slower. You can take a bus to one of the MRT lines in 10-15 minutes and then you’re only a few stops from NTU.
If you tell us the street your townhouse is on we can advise you further.
I agree with Maoman about Mucha (sorry, but I prefer this spelling). The mountains surround us here and there are lots of good, clean hiking trails. If you like tea there are dozens of tea houses in the mountains too. The dikes along the Chingmei river run for many kilometres so if you like to jog, bike slowly, or just stroll you have your place. Jenda university is here too with clean grounds and more hiking trails.
One of my favorite lazy Sunday sunny afternoon activties is to hike up the back of the university grounds, up to a temple that overlooks Taipei city, hang around the temple for a while people watching, then hike back down to the front entrance and stop for Yunan noodles.
Oh, and there’s a little butchery shop here that imports foreign meats, fish and groceries.
When you arrive in August post again on this site and I’ll give you exact directions to some of these places if you like.