There's no major airport in Reggio Emilia.
There is a local airport in Parma (50 km away) with few connections to Rome, Sardinia (during summertime), Paris and London. The town can be easily reached from the bigger Milano airport Linate or Malpensa, from Verona's Valerio Catullo or from the Bologna Airport, G. Marconi.
Being close to Bologna and Milano, the main hubs for train traffic in the north of Italy, it's relatively easy to reach Reggio Emilia by train.
The train station within walking distance from the city center, and relatively safe compared to major cities train stations.
From Milano and Bologna it's possible to book expensive and fast Eurostar trains, or just jump - without reservation - on a Regional train (slower, probably a bit dirty, but definitely cheaper).
Reggio Emilia is located on the Highway A1, that runs from Milano to Napoli, passing by Bologna, Firenze and Roma.
Leaving from Milano the exit for Reggio Emilia is around 130, 140 km south. Coming from Bologna, the exit for Reggio Emilia is aroung 80 km north. The Milano-Reggio highway is usually busy even in the evening and early morning, but it's not so common to be stuck in a long queue for long periods of time. On the other hand, going from Reggio Emilia to Bologna, or passing Bologna, with the highway, can be a pain sometimes, because of traffic and roadworks.
The best Reggio Emilia can offer is all in the city center, so you probably won't need to get a taxi.
Taxi are not so common in Reggio Emilia, it's almost impossible to see one around in the streets. If you need one, you can catch it at the train station, or just make sure to have phone numbers to call one.
The city center is usually very safe, and offers a nice environment for a walk, shopping, going out to eat (from very formal restaurant to a quick slice of pizza).
Definitely the city offers the best at a slow pace walk.