Hi
We stayed Bologna (2 seniors) 5 years ago. City very interesting - nothing like we had anticipated. Surrounding towns - Modena, Ferreira, Parma, Ravenna (bit further away from Bologna) all great to visit. Easy travel to all and between towns by train but note you have a car. Car in Bologna could be a challenge for parking, etc so when booking check this out. With kids, you might want to consider one of the smaller towns as your base & then travel to Bologna & other towns. We had friends who did this and found it easy.
For Tuscany/Umbria, we suggest Bucine. It is about 20 years since we were there but we liked it due to its central location - a few miles off the Rome/Florence main highway but close (easy drive) to Sienna and all the other famous Hill Towns (San Gimignano, etc) but also not far to Arezzo, Corona & Lake Trasimeno and other towns in Umbria. The highway basically divides Tuscany & Umbria.
Agriturismo (farm stay) is great but one warning - be sure to have distance to small town with restaurants, grocery store confirmed before booking as many are out in middle of "nowhere" throughout the hills of Tuscany. We stay in an agriturismo in Bucine - think it is the one in first link below but not 100% sure (too long ago). But, we were within a mile of the town. When looking for place we stayed, found the apartment in the 2nd link - doesn't sound like it is an agriturismo but is very close to town.
Since you are going to Italy in July, the other recommendation is to select and book your accommodation very soon, particularly for Tuscany & Umbria area.
Happy planning and then travels.
Bev
https://www.booking.com/hotel/it/fattoria-casabianca-bucine.en-gb.html
or
https://www.booking.com/hotel/it/il-castello-bucine.en-gb.html
