What kind of hike are you looking for?

If you get a map and look at it, my general experience has been that the northslope generally has a more mild incline. Depending on where you go, you'll still climb, but generally not as much or as steeply. Coming from the south slope tends to be a little steeper ups and downs and maybe even a little more rocky.

I really like the Garfield basin (Spider lake, Five Point lake, etc.) and am going back there this year. What I liked most was we saw no one last time we went there except within 3-4 miles of the trailhead on our way back home. We're looking to summit King's Peak from this area later this summer.

Red Castle is absolutely beautiful, but gets a little more traffic. Of course, there are places you get get to away from the crowds in the area, particularly if you aren't necessarily looking to do any fishing.

I haven't spent much time in the Grandaddy Lake area, but went once and camped at a place called Palisade Lake. There are some campsites there on the west side of the lake which are on a cliff maybe 20-30 feet above the lake overlooking it. Great spot to watch a sunrise. This area also gets a little more traffic, but if you go in a little further you can get away from most of it. This area also has some loops you can take for day hikes while there.

I haven't been to Brown Duck, but have heard a lot of good things about it.

I've been to all of these places as few as 3 days - 1 day in, 1 day out, 1 day messing around in the woods.

I would probably try to go in July or August. September probably wouldn't be too bad. In June there's a good chance you'll run into snow.

For the record - none of these spots are above 12K feet, but you can get there from them.