Hire a water taxi to give you a ride across the bay, bring a rifle, camp gear and a bear tag or two...
Spring for the extra cash and do an extended/long range trip or overnight trip to the Gulf to fish (Chugach Island area). Its a two hour ride out of Homer, but worth it. Don't book a cheap halibut trip. Fishing right out of Homer is way over rated, you'll pay $250-300 to fish with 20 other people and catch a bunch of 12lb fish. Hopefully your trip spans the 1st of july? If so ling cod season is open. Most fun fishing you can have on the salt water, IMO. 20-40lb fish jigged similar to walleye, but the jigs are about 24oz instead of 1/2.
The Russian River will be fishing pretty well in June, depending on when... usually Father's Day is the peak of the run, but opens on the 11th.. A couple hours north of Homer... expect crowds. Fish super early... 2am-7am. Better fishing and avoid a lot of people, but you'll see more bears.
The king fishing will be decent in the rivers north of Homer to Kenai. Hard to say if they'll be open to fish though. King runs have been decent so far this year... been a few years. Usually open on the weekends from first part of June through the end.
Did I mention bear hunting? There are thousands of black bears on the Kenai. Many are accessible off the highway, after a mile of bush-whacking, and 1500 vertical. Get into the alpine and you'll see one or two.
Go to Hope for lunch, take a drive up Palmer Creek Road to the old Swetmann mine. The road is about 10 miles long, pretty neat drive from the valley floor to the alpine.
You could spend a couple days and hike the Resurrection Trail. Start in Hope and come out in Cooper Landing. Its about 35 miles. Pretty easy hike, can be done in two long days or better at 3, with many FS cabins to stay in/rent along the way (book in advance). Snow could be deep at the top of the pass depending on when in June you come, but the trail is prbably broke open. Should see lots of wildlife.
Check out Langille Mountain in Cooper Landing, as well as Cressent Mountain... bring spotter/binos to look at sheep and goats.
Hike to the falls at the Russian River, and then on up to the lakes. Should see bears, and goats, maybe sheep if you are lucky.
Fish rainbows on the Kenai... killer rainbow fishing. Pretty much all the clear rivers are great fishing. Most of the fisherman focus on slamon so you can have it all to your self in some instances. Check regs to see whats open...
Book a charter out of Seward of Whittier... my preference for salt fishing. Scenery is much better, and likely to see a lot more marine critters. Quicker to get into the gulf waters to fish.
Do a "glacier" tour out of Seward or Whittier, boat ride with lunch. They also have Kayak trips as well.
