Obviously depends where you are coming from. We arrived by train from Venice, a mere 1 hour 25 minutes away and a cost of little over 9 euro!
You can fly to Verona from Stanstead with RyanAir (actually they fly to Brescia, but that's how RyanAir works :-S).
Just walk. We walked everywhere and the city is compact enough that you shouldn't wear yourself out. Castelvecchio is a little out of the way of the other sights, but it's still walkable.
The city is easily reached by train from Venice. Trains are frequent, reliable (when there are no strikes) and fast.
I flew out of Italy from Verona. Not many international flights arrive here, so the checking in process was fast.
Bus. There is even a special bus to the airport.
Verona is in easy reach from Rome, Milan or Munich, both, by car and train. Its proximity to Austria and Germany make it an ideal site for a week-end trip.
I used to get there by train from Bologna and Venice
I think there's no other way to getting around but to walk.
oh, the sights you'll see: like the 18th century Basilica di Monte Bérico and 20th century graffitti