Yup, it's a strange, but interesting hobby!
First thing just about anyone who has an interest in it does, is take their geiger counter around and try to identify radioactive stuff. There's really not alot of really hot stuff around (good thing), but once you learn to use your instrument, a bunch of warm stuff does present itself.
Coleman lantern mantles, pre about 1995, are a common one. A few in contact with the tube makes the geiger counter sound alot like radio static. Radium dials, of course, are even hotter. Some ceramic glazes, some bricks, etc. are low level emitters. Background radiation is almost double in my basement (uranium or thorium in the concrete, I live in a low radon area).
The dust on your TV screen is radioactive. It's a result of the decay products from radon collecting there (they have a static charge, so they get stuck to the staticy screen). You can swab that dust, and detect it with the counter, about 5x background at the start. Decays away in a few hours, so with some simple software, you can get a good value for the half life, and make some educated guesses about what isotopes are in there.
I could go on for hours, but noone wants to hear it all. There are lots more involved in this stuff than me, I have so many hobbies I only get middling expertise in any one of them.
You could visit the Yahoo groups "CDV-700 Club" or "GeigerCounterEnthusiasts" to see what folks do with this hobby. Some are fine scientists in their own right, some cobblers like myself!
Thanks for your interest!
J