There is no one best side of Crete, full stop. It depends on what you are looking for: long beaches, scenic coves, mountains, nightlife… However, if I really have to make a choice: Best base to explore: north-west coast.
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It depends on what type of experience you're looking for. The east side of Crete offers more rugged and less crowded beaches, while the west is known for its cosmopolitan cities and picturesque villages. If you want to relax and enjoy peace and quiet, then the East is your best bet.
In general, eastern Crete is warmer than western Crete, the southern part of the island is warmer than the northern, the western part of Crete has more vegetation and in the mountainous areas the weather is cooler.
Chania Town is probably the most beautiful town in Crete. The Old Town of Chania, with the evident Medieval style, is a wonderful place to walk around, lined up with elegant Venetian mansions.
South Crete is generally a couple of °C warmer (but water temperatures are roughly similar). The east of the island, has less rain than the north and especially the north-west.
Elounda is a beautiful simple fishing village in the North of Crete. Over the years it's attracted the worlds rich and famous with the likes of Lady Gaga, Leonardo DiCaprio and the Saudi Royal Family choosing to holiday here.
This means that even when the north coast is uncomfortably windy, the south coast may be calm and pleasant. The exception to this is where gorges and valleys channel the north winds, which can create areas of intense winds at certain spots along the coast. This is especially true at Frangokastello and Plakias Bay.
If you are looking forward to having some quiet time and a semi-rural experience, consider visiting the southern side. However, the more adventurous tourists should go to the north where it is easy to find transportation, modern amenities and exciting nightlife.
July is the hottest month in Crete with an average temperature of 26°C (79°F) and the coldest is January at 11°C (52°F) with the most daily sunshine hours at 13 in July.