The city centre is compact enough to walk. Rua Halfeld, Parque Halfeld, the cathedral, and most downtown museums and cafes are within fifteen minutes of each other on foot. The Museu Mariano Procópio is further out — about three kilometres from the centre — and easier to reach by bus or taxi.
Juiz de Fora has an extensive urban bus network that connects the centre with the university campus in São Mateus and the outlying neighbourhoods. Fares are cheap but the system requires some patience and local knowledge to navigate. Ask at the rodoviária or your accommodation for routes to specific destinations.
Taxis and ride-hailing apps (Uber operates here) are the most practical option for reaching the Museu Mariano Procópio or moving between neighbourhoods in the evening. The city is not large, so fares are reasonable.