How about looking for a correlation between sunspot numbers and various indicators of northern hemisphere weather. You can find the sunspot numbers in one of my questions about the Sun, or by visiting the NASA MIDEX/IMAGE site and looking under the 'activitiies' section. For weather, try averaging the annual rainfall statistics from many dozen non-big city cites across the USA, or the number of hurricanes during the year, aurora, or other major weather events. Using statistics and the methods of hypothesis testing, see whether you can find a correlation or not.