There are a couple of Fly outfits in Cooper's Landing, definitely give them a ring for the lay of the land, I've dealt with Troutfitters a fair bit, they are super helpful and have rental gear if needed.
If you are in Anchorage and have time definitely swing into Mossy's Fly Shop, they'll get you everything you need and have an idea of how fishing is all over the area.
I would highly recommend heading to some of the mountain lakes and streams in Chugach for bows and greyling, Crescent Lake is a nice hike, beautiful and has tons of fish. The moth of Kenai lake into the river is also highly productive but be prepared for combat fishing fri-sun. Rabbit Lake is also great but is closer to Anchorage
I've worked out of the Kenai/Soldotna area on and off for the past ten years now, the fishing and scenery is amazing. It helps to be prepared if you've never been, bug spray, rain jacket, and despite never having issues with the bears (lots of encounters) I'd bring some bear spray and definitely make noise when you see a blind corner on a trail. Also another thing to use to your advantage is how LOOOOOOOONG daylight hours are. I would work a full 8hr day, then go out and hike and fish for another 4-6hrs after work, get home and still have light.
I would suggest bringing atleast one 5wt and one 8wt singlehander and if you can swing it bring a 7wt spey or switch rod, if not get a spare spool and build a singlehand spey rig (like OPST Commando) for both the 5wt and 8wt, there are lots of rocky shorelines with tons of overhanging foliage right up to the bank.
Seward can be a fun place as well, try to get out to humpy's cove and see all the salmon, also be sure to check out the marine life center. The food is pretty decent in town as well, the Thai place is great, and there is a decent greek restaurant as well. Seward will be packed with tourists right now though so have patience.