Since you asked about June, the salmon will probably not be 'running'. That being said, there is a King Salmon run in June. We were invited to go 'early run' King Salmon fishing with our B&B hosts out of Wrangell, on the 30th of May. We also saw some being harvested inland, south of Tok, about a week later.
We saw a 'barn door' halibut leaving the marina at Glacier Bay. Most (virtually all?) of the small communities have charter fishing up and down the coast. We saw 'weigh-ins' while visiting the docks at Valdez and Seward. The Halibut were in the 20-30lb range, with some Rockfish, and possibly Lingcod. These were during the first 2 weeks in June.
Don't sell the Marine Highway short, it is spectacular scenery all the way! I spent most of my time on the outside decks, fore and aft! The only one that is overnight is between Wrangell and Juneau (ignoring Washington to Ketchikan, which is 2 nights), and the sunset over Petersburg is spectacular! I asked to visit the bridge, via the purser, and got permission! It is quite interesting! Much better than flying over all that scenery. Check it out!
If you need to use the Marine Highway, keep in mind they are subject to changing their schedule, they are supposed to notify you if you have a reservation, of any changes. They didn't notify me, but I checked in advance and made arrangements to fly from Juneau to Glacier Bay, with no issues.
We saw our 1st black bear along the Stikine River, several along Tracy Arm, 3 more after disembarking at Auk Bay (turned the opposite way from Juneau, as we were early).
Along the Inside Passage, you will probably have the 'tourist' area's of the towns to yourselves, since there will not be any large cruise ships in port (usually 3 or 4 everyday, with multiple thousands each!).

Approx. # Picts I took at each local, and time spent there (I actually spent more days at each location, but the major areas, and not travel time, are what I am counting here)(since I drove, these were actually over about 20 days): Misty Fjords/Ketchikan 500+; Wrangell and/ferry to Juneau 900 (2days); Tracy Arm 1200+(approx. 6 hours); Glacier Bay 850+ (1 day); Haines 300+ (3 days); Skagway 250+ (1 day); Seward/Kenai Fjords 750+ (2 days); Katmai NP 800+ (approx 6 hours)(guide also tried to find the wolves, just got a fresh footprint)(at least a dozen brown bears); Kenai Peninsula 450+ (2 days).

Since you asked about June, the salmon will probably not be 'running'. That being said, there is a King Salmon run in June. We were invited to go 'early run' King Salmon fishing with our B&B hosts out of Wrangell, on the 30th of May. We also saw some being harvested inland, south of Tok, about a week later.
We saw a 'barn door' halibut leaving the marina at Glacier Bay. Most (virtually all?) of the small communities have charter fishing up and down the coast. We saw 'weigh-ins' while visiting the docks at Valdez and Seward. The Halibut were in the 20-30lb range, with some Rockfish, and possibly Lingcod. These were during the first 2 weeks in June.
Don't sell the Marine Highway short, it is spectacular scenery all the way! I spent most of my time on the outside decks, fore and aft! The only one that is overnight is between Wrangell and Juneau (ignoring Washington to Ketchikan, which is 2 nights), and the sunset over Petersburg is spectacular! I asked to visit the bridge, via the purser, and got permission! It is quite interesting! Much better than flying over all that scenery. Check it out!
If you need to use the Marine Highway, keep in mind they are subject to changing their schedule, they are supposed to notify you if you have a reservation, of any changes. They didn't notify me, but I checked in advance and made arrangements to fly from Juneau to Glacier Bay, with no issues.
We saw our 1st black bear along the Stikine River, several along Tracy Arm, 3 more after disembarking at Auk Bay (turned the opposite way from Juneau, as we were early).
Along the Inside Passage, you will probably have the 'tourist' area's of the towns to yourselves, since there will not be any large cruise ships in port (usually 3 or 4 everyday, with multiple thousands each!).

Approx. # Picts I took at each local, and time spent there (I actually spent more days at each location, but the major areas, and not travel time, are what I am counting here)(since I drove, these were actually over about 20 days): Misty Fjords/Ketchikan 500+; Wrangell and/ferry to Juneau 900 (2days); Tracy Arm 1200+(approx. 6 hours); Glacier Bay 850+ (1 day); Haines 300+ (3 days); Skagway 250+ (1 day); Seward/Kenai Fjords 750+ (2 days); Katmai NP 800+ (approx 6 hours)(guide also tried to find the wolves, just got a fresh footprint)(at least a dozen brown bears); Kenai Peninsula 450+ (2 days).

I assume Juneau as your starting point, since you mentioned southern coast and the inside passage. Mendenhall Glacier is worth the effort, which actually isn't much (effort). Further south, there are side roads to minor waterfalls and streams. If you have time, after you take the 6+ hours inside passage to Skagway, travel up into Yukon and across the southern part to the highway going to Muncho Lake, BC. Lots of streams, waterfalls, and mountains. I captured pictures of red foxes, lynx, buffalo, bears, 3 types of sheep, and reindeer (caribou). If you have sufficient time, it will be well worth it. There is a place on Muncho Lake (Double G Services) that I like. The accommodations are rudimentary but comfortable, and the food there is excellent. Photo of Whirlpool Canyon on the Laird River attached. Enjoy.

Homer is a great place to visit. It’s a small, artsy/craftsy community with a lot to offer. Halibut charters are available, but a bit expensive, but the reward is the best white fish you’ll ever eat. And yes, salmon fishing is more fun because they fight.

Consider driving to Seward and taking a cruise down Resurrection Bay to view sealife and whales, as well as glaciers. We like Major Marine, but Kenai Fjord Cruises is good, also. Another fun location is Whittier. You have to drive through a long tunnel to get there, and it costs $20.00, but the scenery is worth is, and you can go on fishing charters there, as well.

More inland, in the Matanuska-Susitna Valley, a visit to the Hatcher Pass recreation area is a great thing to do. Fabulous scenery, hiking trails, and you can tour the old Independence Mine. You can also visit the musk ox farm just outside Palmer and the reindeer far several miles outside Palmer along the Old Glenn Hwy. For an interesting side trip, you can drive to the end of the Knik River Road to the Knik River Lodge. If they’re still doing it, you can take a helicopter tour of the Knik Glacier. Not only do they fly over it, they also land on it allowing you a short time to walk around on the glacier. Very interesting. Understand that due to Covid 19 they may not be doing this, although things have loosened up a bit up here.

I’d love to go to the Mc Neil River or Katmai to view the bears, but it’s very expensive. If you can afford it, it’s well worth the time and money for the experience. Take a long lens or long zoom. The best times to go are during the peak of the salmon runs in late June and July. That’s also the best time for good weather.

Just a few suggestions.