The short answer : Some provinces & tourist attractions are open again, while other provinces & tourist attraction are still closed for tourists. As usual in Thailand the answer to this question is not so easy. First of all there is a National Emergency Decree and that has recently been extended until 30 June 2020. This means that there is still a nation-wide curfew from 23:00 - 4:00 and that there are still many other restrictions in place. Like that there are still restrictions on inter-provincial traveling. But on the other hand provinces have the freedom to arrange their own COVID19 regulations. So while some provinces are relaxing the regulations others are still holding on to strict regulations. And while more and more hotels, restaurants, shops, beaches and even airports are allowed to open again some provinces are still closed for non-essential traveling. One of that provinces is Nan province in North Thailand. Although the state of regulations can change any day at the moment people coming for tourisme to Nan province are still not allowed to enter Nan province. Hence I do not understand why hotels are allowed to open in Nan province. See also The Nation of 27 May 2020 Nan province tells tourists to stay away for now.
At 25 May 2020 a friend of mine from Norway but living in Nan town did go to Chiang Mai for 2 days. Yes he was checked at the provincial borders. And yes he was checked at entering the hotel in Chiang Mai. And yes he was checked again when entering Nan province. But for the rest no problem. But that same day a group of Thai people from Bangkok wanting to enter Nan province for holidays were not allowed to enter Nan province.
Another example is at 15 April another British friend of mine, living in Nan town, went for a 3 weeks holiday to the beach near Hua Hin. Again yes he was checked at provincial borders and yes he was checked when returning to Nan province. But he had no problem, also not with renting a bungalow near Hua Hin.
Another example is at 20 May a Belgium friend from Chiang Rai wanted to stay overnight in Lampang but all hotels were still closed. Yes he could travel to Lampang and he could travel back again to Chiang Rai. But he could not stay overnight in Lampang.
And on the other hand I did just read that temples in Ayuthaya are open again and visited by both Thai & foreigner tourists.
So yes at the moment of 27 May 2020 it is at a certain extend possible to travel within Thailand. But as every province sets its own rules you will have to check at your destination province if you are allowed to enter and if hotels are open. And you will have to check with you home province if you are allowed to return home. In the meanwhile more and more airports are opening and more and more airlines start to fly again within Thailand. And the same goes for inter-provincial routes for busses.
My personal idea is that this inter-provincial traveling rules will be nationwide relaxed soon and that hotels, beaches and National Parks will be open soon. Although some provinces may still have some stricter regulations in place. And again my personal idea is that once inter-provincial traveling is open then domestic tourism will be booming.