Danshui* is a must-see in the Taiwan tourist world. On Danshui Old Street (淡水老街 / Dànshuǐ lǎo jiē), you can find unique and traditional shops and food such as A-Gei (阿給) and Iron Eggs (鐵蛋 / Tiě dàn). It's nicely situated on a riverside so you can enjoy all this with a nice sunset/nice view.
However, it rains a lot in Danshui, so wait for a clear day in Taipei and then you'll be set for a great day out. As the most north stop on the Taipei Metro, it's only a short 40 minute train ride from Taipei Main Station (that's less than the amount of time it takes me to get to Central station in Sydney...).
After a visiting Danshui countless times over the past few years, I have come up with a few of my favourite things to do/see/eat in Danshui.
My favourite thing to do around the Danshui area is bike riding along the riverside. They have a dedicated bike path making it an easy and scenic bike ride. If catching the MRT, get off a few stops before Danshui at Guandu (關渡). There's a bike rental just outside the station where you can hire a bike for the day from 100 NTD. I would recommend bike riding up the left side of the river to Bali (八里), which is right across the river from Danshui. It should only take about an hour and the left side has less people. If you rent a bike from Guandu, you can return the bike to to their shop in either Bali or Danshui. You can take a ferry from Bali to Danshui (or vice versa) which can be paid for with an EasyCard and you can even take a bike onto the ferry. I personally don't think there's much to see in Bali which you can't see in Danshui, but the ferry ride is quite nice.
However, if you choose to do this bike ride - make sure you keep asking for directions. Even though there's a dedicated bike path, I got lost both times I tried this route. The first time, I ended up with a sprained ankle after dangerously riding on the super busy main road after not being able to find the bike path. The second time, we found the bike path but we rode in the opposite direction for about 20 minutes... So learn from my mistakes - make sure after every turn, you ask someone for directions until you're 100% confident you're going the right way!
For good views of the river, Fort San Domingo (紅毛城 / Hóng máo chéng) would be up there on my list. It's an old Dutch Castle that's open for the public to explore. From the MRT station, you will need to catch shuttle bus red 26 to the castle. You also have the opportunity to get nice and cosy with some hunky men. Who would say no to that?
Besides the traditional food, my favourite thing to eat in Danshui is matcha soft serve. Around the station, you can find lots of vendors selling super long soft serves at ridiculously cheap prices. But in my opinion, that stuff is nasty. If you want a good soft serve, you will need to walk up a bit on the main road (about 10 minutes from the station). Look out for the Ten Ren Tea (天仁茗茶). They have stores all over Taiwan, but as far as I know, this is the only store that sells matcha soft serves. If you're a fan of matcha soft serves, this is the place to go. (Sorry I tried looking for the exact address on Google Maps but I could find it...)
*Danshui is sometimes also romanized as 'Tamsui'. I prefer 'Danshui' because it sounds more like the actual Mandarin.