1. Getting Around Chiang Mai and Chiang Rai: Easiest way is to either hire a private van driver. Alternatively, rent a car and self drive.
2. Speak some basic Thai: Especially, if you would like to ask for directions, bargain, or even trying to blend with the locals, etc. You can do some quick read-up here: Learn Thai Language (Lesson 1) and Learn Thai Language (Lesson 2)
3. Book in advance for High Season: High Season in Chiang Mai and Chiang Rai is during November to February which is the cold season. Chiang Mai and Chiang Rai gets really busy with Thai locals and tourists.
4. Seasonal Weather: Due to its elevated location, the weather in Chiang Mai and Chiang Rai is a bit cooler than the rest of Thailand. Especially during cold season, be sure to prepare some warm clothes, as temperatures can get really low at night. At other times, its mostly hot throughout the year and the hottest time would be April. This is when the Songkran period starts.
5. Weekend Night Markets: Try to schedule your holiday during the weekend for the weekend Chiang Mai and Chiang Rai night markets.