How To Render A Smoother Tile Based Map?

Ok so this is my tile based game. I am using jPCT and the square tiles are code generated objects with a texture applied. I use A* for all translations and that system is built around a tile based region.

You can see in the image how the tiles are jagged looking. How could I make this better? I’ve tried using a triangle based tile terrain but it looked even worse lol.

I would like to replace tiles with hexagons, and retain clipping based on tile data. How can I go about this, or just blending the tile textures in the in-between areas using a magical shader or something?!

Here is a great article about blending textures together: https://web.archive.org/web/20140117045322/http://www.m4x0r.com/blog/2010/05/blending-terrain-textures/
The result looks really good.