Depends if you want to do natural birth or csection. For natural birth I would go to the government hospital in the centre of chiang rai, providing you speak some thai they have a natural birthing course you can enrol in for free and then you only pay a couple of thousand for the VIP room for recovery.
For private I would go to Sriburin hospital. We paid around 60k with 3 nights in hospital. Very professional and helpful, if there are complications and are afraid of the bill you can always tell them and move to the government hospital.
But first of I highly recommend you go to Kultali clinic. She will be able to tell you all these things, the costs and specifics. She speaks extremely good English and will do all the check ups and the delivery of the baby at hospital of choice.
Good luck