Scenic Train ride

I'm looking to see if there are any trains that go between Udon Thani, Mukdahan or Khon Kaen to/from Chiang Mai.  Anyplace around those three cities to/from Chiang Mai that have some kind of train would be nice as that is where I will be for two weeks in March.  I'm looking for a nice scenic countryside tour and to hopefully spend a few days in Chiang Mai.

I know there are several from Bangkok to Chiang Mai, but I won't be in Bangkok long enough to utilize those ones.

I don't want to fly there, but I am open to other suggestions.

I do not think they have trains that run to CM from cities you mention without going all the way to Bangkok.  If you want adventure take a bus.

See this site for train routes and other train info:
railway.co.th/English/network.asp

The short answer to your question is no. There is no cross country link between the cities you mention.

If you are a railway enthusiast and have some time in Bangkok why not travel on Thailand "secret railway."

Its a little known line that runs from Bangkok to Samut Sakhon and then onward to Samut Songkhram. Sometimes referred to as the Mahachai-Mae Klong Railway.

Another alternative is travelling to the River Kwai bridge by train which is a very scenic route and includes parts of the old WWII Thai-Burma Railway.

Details of all train travel in Thailand can be found here.

Enjoy your time in Thailand.