There are uncountable great destinations in northern Italy. The stretch between Venice and Verona (both very worthwhile, of course) includes Padua (spectacular chapel and large historic area) and the smaller, more laid-back Vicenza (Palladian architecture). Once in that area you're not far from the lovely lakes. The Dolomites (train to Bolzano, then bus up into the mountains) are beautiful and especially great if you like outdoor activities. That area (the Alto Adige/Sud Tirol) is culturally Austrian, so it's a bit like visiting a foreign country.
If you'd be interested in a large city with an expansive historic district but not a lot of foreign tourists, Bologna fills the bill. A bonus is that it is a fabulous transportation hub from which you can take convenient day-trips to a lot of wonderful cities. Ravenna may be my favorite small city ever--fabulous Byzantine mosaics, charming architecture, unbelievably few tourists given its attractions. Other folks here really like Ferrara, and there are many other places within reach.
Close enough to Florence for side-trips are Siena, Lucca, San Gimignano, and Volterra. The first two are easily reached by public transportation; the second two might be a bit more of a challenge, but I think it can be done. You might like to rent a car for a day or two (or take a van tour) in order to see some of the smaller Tuscan villages that are not so efficiently reached by bus or train.
Tell us about what sort of experiences you want to have during your honeymoon, and you'll get some more-specific suggestions. Wineries? Art museums? Car museums? Fabulous churches?
With a couple of weeks at hand, I think I'd try to include at least a day or two along one of the lakes, just for the sake of variety. Although you certainly could pop over to Austria or Switzerland, I'd be inclined not to spend the time to do that on this trip, given the vast number of great options closer to hand in Italy itself.