Absolutely! Travelling to these diverse and vibrant South African cities could make for an unforgettable experience. Here are some travel tips for you to consider:

Best Time to Visit:
The best time to visit Johannesburg and Bloemfontein is in the spring (August – October), when the weather is mild and the city is in bloom. For Cape Town, the ideal time is during its warmer months (November – March).

Route and Accessibility:
Each of these cities can be reached by flights from major international airports. Domestic flights are common between these cities as well. Car or bus transit is also available, but can be a long journey.

Altitude and Acclimatization:
Johannesburg is fairly high in altitude at 1753 meters, so give yourself a day or two to acclimatize, particularly if you're sensitive to altitude change. Bloemfontein and Cape Town are at lower altitudes.

Accommodation and Booking:
All three cities have a broad range of accommodation options. Early booking is advisable, particularly during peak season (December – January).

Clothing and Essentials:
Light clothing for warm days and heavier items for cooler evenings would be suitable. Sunscreen, hats, and sunglasses are recommended due to strong sunlight. Walking shoes might come in handy in Johannesburg particularly, for exploring its city streets.

Health and Safety:
Stick to the busy areas, particularly after dark. Check in advance regarding safety precautions for each area to ensure you take adequate precautions.

Local Etiquette and Respect:
South Africans are generally very friendly and informal. However, remember to respect local customs and etiquette. Use polite greetings, and respect diversity. Each city hosts numerous cultures with their own unique traditions and customs.