Welcome to Alaska! I won't be able to meet up with you (I'll be there for part of the summer but will be leaving a few weeks before you get there), but hopefully some others in town will be able to meet up. It's a bit far out for most to confirm, so you might want to bump this thread closer to your date of arrival to remind them you're coming and to schedule something.

I'm personally not sure the best place to deal with kayak rentals would be. Are you more interested in kayaking on a lake (I've gone out on Eklutna Lake before, which is a beautiful hidden gem near Anchorage) or out on the ocean? If the latter, I don't think there's much in the way of kayaking near Anchorage due to the tidal mud flats and lack of easy ocean access. Most kayakers go out of Whittier, Seward, or Homer, and you might find more in the way of kayak rental outfits in one of those towns.

As a decent general all-around source for Alaska info, check out http://www.alaska.org. They may be able to point you towards some resources for that.

For other equipment, there are a few places in town to check. The biggest name is probably REI, but there are probably some local places that rent as well. I'm not up to speed on that, though.