MIKE MOSS SAYS: Tony, As a rule of thumb, those really aren't too bad, but many times the word "always" causes trouble in meteorology, or most any complex process that involves the interaction of a lot of contributing variables.
I would probably re-word your first statement to say that in the northern hemisphere, tornadoes usually travel toward the northeast. There are numerous examples of tornadoes that travel east, southeast, and northwest for example. However, the large scale atmospheric patterns that are most prone to encourage the formation of tornado-producing thunderstorms are those that involve low to mid level wind fields that produce a storm cell motion toward the northeast, and that pattern often holds true for twisters here in our state as well as most other in the country. You might enjoy looking over a clickable map of tornado tracks for a part of Kentucky and Indiana. You'll see several with easterly or southeasterly tracks, at
So, a tornado following the most common path in Cary would tend to move northeast. To avoid it, however, I would be more inclined to travel southeast from Raleigh or Clayton (making a right angle away from the path of the funnel) rather than northwest or west. Here are some links to track maps from a few NC tornado events...
And here's an example of a NC tornado that moved northwest (scroll down to the Moore County)
As for the rain rule, the same general discussion applies. There is often a mostly rain-free area in the vicinity of a tornado formed by a supercell thunderstorm, but again, there are exceptions to the rule in which tornadoes have plenty of rain and/or hail in the immediate vicinity.