Been there many times and really love it. The art galleries in particular. Not sure what it's like with online advance booking these days but there was a fair bit of queuing at more touristy times of year last time I was there in the Easter hols in 2012. Not sure what to suggest re kids that say they don't like art galleries and museums. If the rest of you want to go then a tween can surely just go along with it.
Top sightseeing for me - Duomo, Academia, Uffici, Bargello, Boboli Gardens (but if it's hot there it too much), Pizza on the Ponte Vecchio, Leather bags at various markets and sometimes glasswear and jewellery, Santa Croce, Santa Spirita, Santa Maria Novella, English Bookshop, Piazzale Michelangelo, Markets.
There's a Da Vinci museum with interactive exhibits that I've not been to but hear good things about.
Restaurants etc - Ice cream, Pizza, near the leather market there are some good ones