Mantua

I believe they still have a lot of damage from a relatively recent earthquake that means a lot of the major sites are still closed. I suggest researching that further before you go.

I spent nearly two weeks in the Veneto and Bologna and surrounding areas last year and for me and my wife the biggest letdown was Mantova.

There's a lot of industry spoiling the lake area, the Palazzo Te - for which we had made our trip - was much more plain than I'd expected and although we were practically the only people there it didn't seem worth while.

There are many cities nearby that we absolutely love - top of the pile for western Veneto is definitely Vicenza at which we would happily spend another month, and several more days in Verona would be lovely.

I stayed in Mantova a few years ago and enjoyed it very much. Have you been to nearby Ferrara? Either makes a good daytrip from the other. Ravenna is not far, either, if you haven't been there yet. All are much less visited by swarms of tourists (unlike Verona, which I also love but I offer it as a comparable destination).