There are several black bears in the Juneau area, as well as a few brown bears. This said though, bears are not typically a large concern when running in Juneau. In 8 years of running trails around Juneau I have seen fewer than a dozen bears while out on runs. They generally know where we are long before we know where they are, and they generally disappear well before we see them. There are however some basic tips that should be known when running in bear country and we will go over these before we hit the trail the first day.
Juneau is known for it's rain. Downtown receives almost 100 inches of precipitation a year. The good news is that Summer is typically the driest time of the year in Juneau. There is a chance that we will have beautiful sunny weather all week. The bad news is that there is also a chance that we will have cloudy rainy weather all week. Fortunately it doesn't often rain very hard in the Summer in Juneau, rather a slow steady drizzle. With the right attitude and the right gear the rain is rarely much of a nuisance. Best thing one can do is show up with the mentality that it might rain for a week straight and to accept that ahead of time. It will make it much easier to cope with if it does occur, and it will make any sunny weather even that much more enjoyable.
Leave your headlamp at home. In June we will have about 20 hours of usable daylight per day! The July session will have a bit less daylight, but still enough that we will never be dealing with being out on the trails in the dark.
Temperatures will be in the 50-80 degree range (10-15 degrees cooler up in the mountains). Keep an eye on the weather forecast as your session gets closer, but I would highly recommend bringing clothing (both running and casual) to cover this range of temperature.
There is water everywhere around Juneau. You are never more than a few minutes away from water sources. I (and virtually everyone I know) drinks water straight from the source, without treatment when in the mountains around here. This is generally safe as there is essentially no development in the area much above 400 ft. above sea level. As soon you go a few minutes up the trails you are above potential contaminants. This said, If you feel uncomfortable with the notion of drinking water straight out of streams, glaciers, snowfields, and rivers be prepared to carry enough water for 5+ hours out on the trail, or some means to filter/treat the water. Either option works great and is simply a matter of personal preference.
Besides being the driest time of the year, and the lightest time of the year, Summer is also the best time of year for running the ridgelines around Juneau. There will still be quite a bit of snow left in places above treeline (especially during the June session), but it will be consolidated snow that is great for running on. It evens out normally rocky surfaces and makes for very smooth, efficient, and fast descents. The one concern with running on the snow is that it tends to be very crusty and sharp on the surface. When you descend on sun exposed areas you may dig through the top layer a few inches and cut up the skin on your lower shins. There's a simple remedy to this: socks that come several inches up your shins. Small running gaiters will also help with this, as will running tights/pants (but if it's 70+ degrees these might not be the most comfortable option). I highly recommend having at least one of these options with you on each run we do up on ridges. This won't be as much of an issue for the August sessions, but if it's a big snow year and/or a cool summer we could be doing a fair amount of running on snow in those sessions as well.