Lamphun is only 1/2 hour from C M, and the most interesting route is along the big trees. Can catch a songtheaw from the market. Used to be a small bus too, perhaps still going.
Otherwise big bus from bus station down the expressway.
Not noted for 5 star hotels and there is one ancient temple to look at. Not a place to see by walking, so rented car perhaps.
If having a rental, can go to see temple that was in the Rambo movie. High on a hill with great views. Temple of the footprint is below.
Best combined with a trip around the MHS loop. Don't know if buses are available the entire loop, and not at all from MHS along the northern route. That was by van only. I know a songtheaw from C M passes by the Doi Inthanon turn off.
Frankly, I can't see any benefit from trying to use buses, as most of the sights are off the main roads.