Neighborhood to Stay in Taipei?

What would be a good neighborhood to stay in for a first trip to
Taipei?

We like to stay in a very good hotel, then to walk around near the
hotel, and see shops and restaurants and tourist sights with the
flavor of the city.

We are not so interested in modern shopping malls or night life.

People have suggested to us to stay near the World Trade Center, but I
wonder if that area is just all modern like any big city. (I've never
been there so I don't know.) And the Grand Hotel looks exactly right
for us, but reviews on line say it's not easy to walk anywhere from
it.

Is there someplace more like what we want?