Tamsui is the mouth of the river and is 1 hour from central Taipei by subway. Taiwanese usually come on Saturday or Sunday to spend the day. That is why on weekends there can be too many people (be careful when returning by metro, better let the previous one pass and get the first of the next to find a seat).
During the week renting a bicycle and doing the whole ride enjoying the sea breeze, without being the best of Taipei, is a plan. When leaving the metro station, towards the river on the left you will see a rental stand. Although it is a good time you can get to the port with the Tower and the Bridge of Lovers (Lover's Tower and Lover's Bridge).
In our Taiwan Travel Guide you have all the information you need to visit Tamsui.
Here we indicate the best restaurants in Tamsui.