Hey - greetings from an Alaskan turned Seattleite! There is some good climbing in the general Anchorage area, including some decent stuff just south of the city on the Seward Highway. If you want hard sport, Wiener lake. There's also Ravine Lake and, most importantly, Hatcher Pass. Hatcher is a great big mix of granite sport, slab, and trad, with Index type ratings on the trad. Your best luck in finding a partner would be to check out the Alaska Rock Gym, known as AGR. Lots of great climbers train there as its the only real gym in town. Also, check out Alaska Mountaineering and Hiking, or AMH for short. Great spot. You can also drive down the Seward Highway and stop when you see climbers, as most of the climbs are roadside. I have met a ton of great people doing that.
Two great spots on the highway that actually have an approach (5 minutes, no biggie) are Crack in the Woods and Pivot Point. These spots are in the woods, they're beautiful, and the stone is pretty good. There's almost always people at those spots. And, if you're comfortable on 5.4-5.6 terrain, you can solo Sunshine Ridge. It's about 300-400 ft of good rock and a great little solo with the most amazing view. Climb a grassy ramp from the left side of the formation and you'll gain a ledge type feature with telephone/power lines on it and start up the rock. Staying around the middle will keep it easy, the further right you go it becomes 5.7 or so, still good though.
Well, I hope this is helpful for you and you find a way to get some climbing in. If you're down to climb when you get back I'm always looking for partners!
Cheers,
Marc