Chaingmai is a city full of temples, and the sheer number of these temples can be overwhelming. The main temple complex in the old city is known as Wat Chedi Luang and this is the must visit stop for most tourist, but it's certainly not the only, or even best option. While the Wat Chedi Luang is very beautiful, particularly with the very large old temple in the center, it can be very crowded and it can be difficult to enjoy the serenity that temples often offer. The best way to enjoy the Wat Chedi Luang is to arrive very early in the morning, or better yet wander the temple grounds about an hour before closing at night.
As far as the other temples in Chaingmai are concerned discovering them is the best part. Simply wandering through the streets in search of temples is a great way to see the old city and also find some great hidden gem temples. When you're visiting a temple, make sure to be respectful. Take your shoes off before entering any buildings, and consider making a donation to help keep the temple in good condition. I tend to wait till I'm leaving a temple before I make a donation. This way I can see if the money seems to be going towards actual maintenance or not.
Some temples also offer items for sale, or even services (sometimes free sometimes for a fee). The items can be foodstuffs, religious items or flowers to make an offering. The services can be a consultation with a monk, or in some cases massages. At some times you may notice what looks like a cafeteria line forming in a temple. This is a free service where the temple feeds people. This service is available for everyone including tourists, the poor, as well as locals. The best tip for this is feel free to take what you'd like, but don't be greedy.
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