To cover all these places, you can take a taxi, bus or Uber. Taxis are available throughout the city and Uber is also a popular option. Local buses are the cheapest mode of transportation but can be tricky to figure out if you are not familiar with the city. Expect to spend around $15-$25 on transportation.
If you have more time, you can explore other interesting places like Montevideo's beaches, the Legislative Palace, or the Botanical Garden. If you have less time, you can skip the Museo del Carnaval or choose other places to visit. Wear comfortable shoes for walking and bring a hat and sunblock if you visit during the summer. Finally, if you're traveling to Montevideo during February, you can't miss the carnival festivities!