Leave Chiang Rai ?
Apart from flying to Bangkok or Phuket, you can only leave Chiang Rai by bus. The nearest railway station is in Chiang Mai, the train does not go to Chiang Rai. The city has two bus terminals, Terminal 1, in town, for trips in the province (only Green Bus offer long-distance departures from this terminal) and Terminal 2 for long distances. A bus ride to Bangkok takes at least 11 hours, so the plane is strongly recommended. There are otherwise buses to Sukhothai or Phitsanulok and some other destinations without going to Chiang Mai first. To return to Chiang Mai, since the only possibility is to take a bus from the Green Bus company, if you do not want to end up waiting 2-3 hours at the bus terminal I advise you to buy your seats in advance, at least the day before you leave
(online booking possible here
but note that tickets are only on sale 4 weeks before the departure date). There are different levels of comfort, the cheapest bus (no toilet) leaves at 9:30.