Agree that Cortina/the Dolomites would be a good option that time of year. We went in the summer and the kids loved all of the hiking/outdoor options. And a hotel with a pool would be a plus.

Tuscany or Umbria would also be beautiful that time of year. Depending on where you go, there are dozens of beautiful towns to see and lots of great hotels with pools and amenities for kids.

Verona is very cute but not a ton to do with kids. Lake Garda would definitely be chillier that time of the year but your kids are at an age where they might enjoy Gardaland.

We were at Lake Garda in mid-Sept and it was a beautiful time to be there but I wonder if mid-October might a little too late to enjoy it. You don’t need to swim, but I think it would help if it’s not too cold to be on the water or to eat outside.

Verona would probably be a good stop. Maybe (in the other direction) Trieste— but that’s also a little better in good weather. The mosaics in Ravenna are incredible but up to you how much your family would enjoy them.

If you like outdoor activities in the mountains Cortina might be nice because they also have beautiful hotels with indoor swimming pools and spa amenities for you if that is of interest to your kids. I love Tuscany. Bologna is a university town and not really suited for vacations. The food is a little more interesting than other areas and it’s known for theater but Inwoulsnt prioritize it over Tuscany.

We have a week in mid-late October and are consdering a week in northern (or northern-ish) Italy. Where would you go for an additional 3-4 nights after 3 nights in Venice? We could also stay an extra day in Venice if that's worthwhile, I just figure a week is too long. Is Lake Garda worthwhile at that time of year or not since swimming would not be an option? Or should we head south to Bologna, Ravenna, or even Tuscany (but not Florence)? This would be with 2 ES-age kids.