Is there any decent closet light that operates off batteries. I had one
That you push, but it didn't give much light. There is no power supply in my closets?

Here are many different styles to choose from. I see in the list 6 inch and 12 inch fluorescent lights. One or two of those should be plenty for any size closet.

The new high output LED lights are good also and produce a bright light on very little electricity so your batteries can last a long time.

Here is a list to compare prices and features.

Battery Operated Closet Lights - Home & Garden - Compare Prices, Reviews and Buy at Nextag - Price - Review

Some of the newer LED's work pretty well but to get a lot of light you will need to pull a wire into the closet. I just added one for my daughter and we pulled a hot from the wall switch into the closet and then ran a small piece of conduit to an enclosed fixture with a CFL. Works great. Good luck.