Depends a lot on what you wish to fish for ...
The biggest draw on the Peninsula of course is the Kenai king ... you often have to put a number of hours in to catch one, but when you do it could be very big!
I think the biggest asset / selling point of the Peninsula is that no where else in AK will you find such a variety of fishing and activities in the same area.
You want the best numbers of kings ... go to the Nush, but don't ever expect anything more than 35 lbs., most are 15-18. It has gotten busy yhough, many call it the little Kenai.
Halibut? Dutch Harbor.
Rainbows? Iliamna area.
Reds, perhaps the same ...
Saltwater-only? Sitka or Craig.
Alaska is a huge place and you must decide a little what you want out of your trip before you can say "this is my spot" or "that is my spot".
The end of May can be a good time on the Peninsula in two guided fisheries: saltwater for kings (more of a bonus, don't expect hot action) and halibut; and Kasilof early-run kings. Not big, but good fighters and essentially the same as a "springer" in body composition. You can often hook pretty good numbers of fish.
On your own, you're gonna be one week too early for the little streams to be open as I recall for any king fishing. You can fish off the bank on the Kasilfo around the hatchery creek (CRooked Creek). 95% of the fish here are lined off the bank, so if that's not your cup of tea, you might consider that.
Unfortunately, too early for reds or river trout fishing, but you can try a number of local lakes for stocked plants. Stop by Soldotna ADF&G for a list. Look for things stocked next spring as I think we'll likely see a pretty good winter kill this year and not many holdovers in many of the lakes with the cold weather so far this winter.
Keep the wife happy and make sure you take her on a Fjords Cruise