Absolutely! Travelling to these Greek sites will make for an exciting adventure. Here are some practical travel tips for your trip:

Best Time to Visit:
The best time to visit these Greek destinations is between April and October to avail the best weather.

Route and Accessibility:
Sparta can be reached by KTEL buses from Athens which will take about 3-4 hours.
To reach Monemvasía, you can either take a bus or drive from Athens which could take you 3.5 - 4 hours.
To access Hydra, you can take ferry from Pireás that lasts 1.5 - 2 hours.

Altitude and Acclimatization:
As Sparta, Monemvasía, and Hydra are not located in high altitudes, acclimatization isn't a concern.

Accommodation and Booking:
There are a variety of hotels and guesthouses available in all these destinations. Booking in advance is recommended especially in peak tourist seasons.

Clothing and Essentials:
Greece can get hot, so pack light, breathable clothing, but also don't forget a light jacket and scarf for the evenings or cooler days. Comfortable walking shoes are also important as these destinations offer many archaeological and historical sites to explore on foot.

Health and Safety:
Carry your essentials like sunscreen, hats, sunglasses, and a refillable water bottle. Good hydration is considered to be key for good health in the Greek climate.
Also, travel insurance is always a good choice before travelling abroad.

Local Etiquette and Respect:
Greek people are friendly and like when tourists respect their customs. Orthodox churches require modest currently so no bare shoulders or thighs. Also, tipping is considered good etiquette in restaurants and cafes.