Sure, I'd love to help with your trip to Vejle, Randers, Haderslev in Denmark!

Best Time to Visit:
The best time to visit these cities in Denmark is from May to August when you can enjoy the pleasant weather with temperatures ranging between 15° C to 25° C. The summer season also sees several festivals which you can enjoy.

Route and Accessibility:
You can fly into Copenhagen or Billund airports and take a train to get to these cities. All three cities are well-connected with trains and buses. Punctual and efficient public transportation is available, making it easy to travel around.

Accommodation and Booking:
Booking a hotel in advance is advisable, especially during the high season. A wide range of accommodations, from budget to luxury, are available. Websites like Booking.com, Expedia, and Airbnb give you numerous options to choose from.

Clothing and Essentials:
Pack layers for the unpredictable Danish weather. Even during the summer, an occasional rain shower can occur, so a waterproof jacket is recommended. Don't forget your comfy shoes for walking, and sunblock, hats for the sunny days.

Health and Safety:
Denmark is considered one of the safest countries, but it's sensible to have health insurance for the duration of your stay. Tap water is safe to drink. Carry a basic first-aid kit with any personal medication needed.

Local Etiquette and Respect:
Danes value punctuality, so be on time. Tipping is not mandatory but appreciated for good service. Respect for the environment is important and littering or not following public park rules can be frowned upon.