Hello! That sounds like a fantastic plan! Traveling to Schengen, Remich, and Grevenmacher will be a great experience. Here are some travel tips that will help you out.

Best Time to Visit:
The best time to visit these destinations is during the summer months of June through September when the weather is warm and pleasant. The spring months of April and May can also be a good option when the countryside is in full bloom.

Route and Accessibility:
The most common and economical way to reach these destinations is by flying into Luxembourg City's Findel Airport and then taking a short drive or public transportation. Schengen, Remich, and Grevenmacher are all easily accessible by road and train.

Accommodation and Booking:
You can find a range of accommodations in these areas from luxury hotels to more budget-friendly guesthouses. It's advisable to book your accommodation in advance, especially during the peak tourist season.

Clothing and Essentials:
The weather in these regions is generally mild, but can vary. Pack a mix of light clothing for warmer days and layers for cooler evenings. Don't forget an umbrella or raincoat in case of unexpected rain showers. Also, consider packing comfortable shoes for walking tours.

Health and Safety:
Europe is generally safe, but it's always important to be cautious. Secure your belongings, be aware of your surroundings, and follow local safety guidelines. The tap water in these areas is safe to drink, but if you're sensitive to changes in water, consider bottled water.

Local Etiquette and Respect:
Luxembourg is a multicultural country, but basic courtesies are the same as in most western countries. Locals appreciate punctuality, brief greetings, and respect for local customs. Learn a few key phrases in Luxembourgish or French to interact with locals.