I thought I'd share the details of this project since it's been running fine for several months now.
There are two versions - one that uses the RFM22B transceiver (433kHz), and another that uses the nRF24l01+ (2.4GHz).
The solar stuff is mostly off the shelf Adafruit parts and it's working great.
The Geiger part can pretty much be any open Geiger or it can be replaced with other sensors.
Build information and sketches are here.
John
Why radiation?
Why radiation?
Because it may be harmful?
@Coding Badly
Why "why radiation"? It's become pretty common to measure background radiation as just another parameter of the weather. Since the Fukushima disaster several global monitoring networks have sprung up. This is due in part to a mistrust of government readings, the desire to have something more localized, and just for the hell and fun of it.
Personally I'm interested to see the daily max radiation even more that then the max temp and humidity.
I hope this answers your question.
Well, it makes more curious...
Is the Geiger tube exposed to the atmosphere (are there vents in the box)?
Have you seen any radiation spikes?
Is the radiation level different at night? (it almost looks like the level is a bit lower during the day)
@coding badly
I find it interesting that your questions seem to relate to the usefulness and validity of this project. 
In any case, here are some quick answers . . .
The GM tube I originally used (shown in the pictures) was inside the plastic case with no vent holes. (It's a weather proof enclosure.) Nonetheless, there is no problem detecting highly penetrating gamma radiation. (Shipping containers are "x-rayed" with gamma.) The tube would also pick up some strong beta.
Later I replaced that tube with one capable of detecting alpha. Since alpha can be stopped by a piece of paper, I mounted that tube with the alpha window sticking out of the bottom of the case. I used gaskets to keep it weatherproof.
With both tubes I get similar variations in the daily counts as well as spikes. Since the creation of radiation is a random process, you have to be careful about making assumptions based on small variations. (I have not noticed a correlation between counts and time of day.)
I do get spikes every so often. What they might be related to, is an area of speculation I won't go into here. However, it's common to try to correlate spikes to the position of the jet stream, and solar activity.
The detection of radiation was only one facet of this project, the solar power budget, use of the transceivers, and logging are some of the others.
I've created many projects with the Arduino, and this was one of the most satisfying. Hopefully, some of the pieces and concepts may be useful to others.
bHogan:
I find it interesting that your questions seem to relate to the usefulness and validity of this project.
I don't understand. Wouldn't usefulness questions be more like these hypothetical questions...
Do you stay inside when the radiation is high?
Did you include a radiation sensor because, being in Colorado, you're concerned about exposure to the sun's radiation?
Have you positioned the sensor at different places on your property in a search for hotspots?
...all of which, as far as I'm concerned, are your personal business.
And wouldn't any self respecting set of validity questions have to include: "What did you pay for it?"
In any case, I hope I did not offend you. I really am just curious.
The detection of radiation was only one facet of this project,
It's also the facet that didn't get much ink on your blog. Which is why I was curious about it.
the solar power budget, use of the transceivers, and logging are some of the others.
And I truly appreciate those facets of your project and your willingness to share the details! I hope to build something very similar for my wife. I have the same sets of radios and am so very grateful that you've published your testing results!
Hopefully, some of the pieces and concepts may be useful to others.
It has already been useful to me. Thank you.
Well done project!