5-day itinerary advice

I'm looking for some advice on an upcoming trip to Switzerland in July.

My current itinerary is as follows:

• Day 1: Arrive in Zurich by plane from Toronto at 6:30am. Immediately travel to Lucerne to use as a base. Explore Lucerne
• Day 2: Mt Rigi. Boat to Vitznau. Cogwheel up and then Cable car down to Weggis.
• Day 3: Explore Lucerne (Swiss Museum of Transport)? Should this be replaced with Zurich since we'll be exploring Lucerne on Day 1?
• Day 4: Day trip to Interlaken & Grindelwald
• Day 5: Explore Lucerne (Swiss Museum of Transport). Hop on and off boat/train with Tell pass. Any recommendations?
• Day 6: Depart for Zurich Airport

A few things to note/questions

• I plan on buying a Tell Pass and using Lucerne as my base. That said, I doubt I need to stay in Central Lucerne, do you have any recommended areas for more budget friendly hotels or vacation homes?
• I will be travelling with my 9-year-old daughter, so we're trying to keep things at a reasonable pace. A short hike (30 - 60 mins is doable). Things like boat and train rides excite her. Even a nice playground will keep her busy.
• Generally, we have no real issue spending an 60-90mins commuting for our day trips.
• We're not opposed to changing hotels, but I figured using Lucerne as a base is best with a 9-year old.