I live about an hour from Verona. This is the site I use for booking hotels here in Italy: http://en.venere.com/italy/. Hotel prices vary quite a bit here in Italy depending on exactly when you’re here and what’s going on in a given city.
In Verona, you might consider the Novo Rossi. It’s a short 5 minute walk from the Porta Nuova train station, and about a 20 minute walk to the old town. Right now, it’s expensive because the horse show is in town. It’s often in the 80 – 90 euro range. I stay there sometimes when I have an early flight from the airport.
Venice is one of the most expensive places in Italy. If you use the map function on the Venere site, look in Cannaregio Ovest for places near the station. Right now, there are a number of places that are within your range though. The less expensive places are mostly near the train station or on the Lido or Murano islands. If you’re coming during tourist season, you might also consider staying in Mestre on the mainland and taking the bus across the causeway into Venice.
In Florence, look in the Santa Maria Novella area where the main station is. Florence is small enough that it’s easily walkable. Hotel California near the Accademia (where David is) might suit your needs: http://en.venere.com/hotels_florence/duo… An even better option might be: http://en.venere.com/hotels_florence/duo…
In Milan look in the Stazione Centrale Ovest and Est areas. You can take the metro to get to the area near the Duomo. You might consider the hotel Terminal http://en.venere.com/hotels_milan/centra… or the Hotel Garda: http://en.venere.com/hotels_milan/centra…
Again, the prices vary a lot – I hope you find something for the period you actually plan to be here.

There is a “Hotels Combined” search engine in the website referred below, which lists hotels by tariff, star and gives all details – like address, map, picture, etc. You have to input the City or Town, Checkin & Checkout dates and click “Search”. You can get a quote in a currency of your choice – Euros, USD, GBP, etc. The “cheapOair” search engine is also very popular. You can browse, compare and book online.