Cloud cover will make your eclipse experience dull, so the main thing for seeing the eclipse is to aim for clear skies. Weather is, of course, impossible to forecast far in advance, so as the day approaches you'll have to play it by ear; but this page hopes to give you at least a general idea of where the best viewing might be.
This page is based on the forecast provided by Jay Anderson; his page has a lot more detail, and maps of the weather prospects along the eclipse path, so it's well worth a visit.
To really experience a total eclipse, you need a clear sky; an eclipse seen through clouds is better than nothing, but still pretty dull. So when planning your eclipse excursion, aim for a point on the path of totality which offers the best chance of clear skies.
There's no way to forecast what the weather will actually be on the day, but we can look at average cloud cover for August and see where it tends to be clear. The good news is that August is a good month for blue skies; human observers typically record no more than 15% overcast days along most of the eclipse path. Still, it may pay to try to get somewhere with a better record of clear skies.
Unfortunately cloud observation is a very tricky business; various methods of observing clouds produce very different results. Satellites might pick up high, thin clouds that humans don't see. Also, cloud doesn't necessarily mean complete overcast — in fact overcast percentages as recorded by human observers are significantly lower than satellite-based figures (but also very variable!).
Below we list chances of cloud cover at various locations based on satellite measurements. These record typically higher numbers than the human-recorded overcast days, but should be useful for comparison as they ought to be more consistent from place to place. Based on these figures, the most favourable area is generally the west of the US; Oregon (not the coast), Idaho, central Wyoming, and western Nebraska are the best bet.
So take the figures below as a general guide, but remember that this is the weather we're talking about — on the day itself, anything could happen. Keep an eye to the forecasts as the day approaches, and be prepared to be mobile if you can.
Oregon's famed cloudiness really only affects the coast, as the Coast Range mountains keep the interior fairly clear. So for eclipse day, the coast is likely to be a bad choice; it would be fantastic to watch the total eclipse come rushing in over the ocean, but the average cloud cover is 60%. Farther inland it drops rapidly; Salem has 45% cloud, and across the Cascades in Madras, the average is down to 40%. Even the Cascades themselves offer a good clear sky record, and might make a superb vantage point. Cloudiness rises again in the Blue Mountains, but falls once again below 40% around the Snake River.
The mountains are generally cloud-makers, so the Salmon River mountains and the Wind River range are poor locations, with cloud cover pushing well over 60% in the Wind Rivers particularly. Idaho Falls is a better place, with 45% cloud, and Riverton WY is about 50%. The Laramie Mountains again raise cloud cover over 60%.
Nebraska generally offers good viewing, with cover as low as 50% in Alliance and points east; Grand Island still has cover just over 50%, so offers fair prospects.
From this point on, though, cloud cover generally rises across the country. St, Joseph MO has 55%; Festus, MO is up to 65%. The shadow of the Ozarks produces a slight relief for Carbondale, IL (very close to the point of longest duration), but even here the cover is 60%.
After this, it gets steadily worse. Nashville has 70% cover; and Columbia, SC has over 75%.
It seems that the Atlantic coast offers more hope to eastern eclipse chasers, as the average cloud cover falls to 75% in Charleston SC, and drops towards 60% right on the coast. You need to watch out for hurricanes here, but the odds of a hurricane on a given day in August are pretty low.