ROSIEPINK gives you a tutorial on how to make a felt pod. (Start with a little bowl, but then think CAT CAVE!) Well-illustrated, very thorough, and points out how to deal with the common pitfalls. One big trick: You work it as a flat disk with a piece of resist in between the two layers!
Cat tree - for real. This would look great in the house, much more decorative than the carpet towers sold at the pet centers, and the kitties seem to be enjoying it! Craft store tree, handyman platforms, totally do-able.