but hard to beat the location, transportation, mountain and lake views, and amenities of a large city when travelling with a toddler?
I would disagree with all of those, except "large city".
Location - working city at the far extremity of Switzerland.
Mountains - It isn't in the mountains, you see them in the distance.
Lake views - it is a big lake, with many other places on it (Lausanne, Montreux to name two). Plus lots of other lakes in Switzerland.
I would strongly recommend you investigate Luzern as your base. It ticks all your boxes ("lake view, nearby a train station, and charm of the City"). Lake and mountain trips nearby. And it has a central location for trips from the station.
Luzern tourist info including hotels: https://www.luzern.com/en/
360° view of Luzern: http://tour.luzern.com/360/en/
Sorry if that isn't what you ask. This forum is a bit "robust" and we try to guide people who we think may be asking the wrong questions.