Upvote:2
How do you plan to enter and leave Thailand? By plane to and from Bangkok, I guess. If so then Bangkok can easily be your first or last. Pattaya would sensibly be the other of these two since (assuming that your flight uses the new airport) it is almost as easy to go between the airport and Pattaya as central Bangkok. The other two are more challenging. They are both considerably further. They are in different directions from each other and from Pattaya. You will almost certainly have to return to Bangkok to get to them. So, you will need to be in and out of Bangkok multiple times. The sequence of the visits won't make much difference.
You could visit all of those places in 14 days but you would spend quite a lot of your time travelling. Consider dropping one so that you can appreciate the others more. Maybe Phuket since you have two beach resorts in your list. Bangkok, Chiang Mai (note spelling), and one beach resort will be very different. Comparatively, Phuket and Pattaya will be similar.
Addition
What I call the new airport is Suvarnabhumi. This is the one close to Pattaya. Assuming that, go to Pattaya first on arrival. This is quick and easy. Return to Bangkok, make side trips to Chiang Mai and Phuket if desired. These will be longer and harder.
There is the older airport Don Muang. This is used for some short, budget flights. It is not so convenient for Pattaya. If you are coming from far away, you will probably not come here. You might be able to get Phuket and Chiang Mai flights from there. From Central Bangkok, the effort to get to either airport is comparable but they are in quite different directions.