
I went to Kodiak Island with my mom. We did mom and son things, nothing to crazy! I was able to explore the town and the more touristy side of the island.
This trip started and ended in Anchorage, but for the purpose of this post it started and ended at the ferry terminal in Homer, a 4 hour drive from Anchorage, but there are options to fly or even take a bus! This post ended up being more of a short review of the places that we visited than details about the trip.
Note: all boats in the fleet are different! We were on the Tustumena. That is the only boat that I have been on and is the only boat that I can speak about.

Unfortunately I don't go on boats often. I went on lakes growing up in the Midwest, but almost never the ocean. The ferry was one of the highlights of the trip for me. The loading, the unloading, the voyage, it was all amazing! We went from Homer to Kodiak on a very calm day, 1-2ft seas, and could see for miles. We saw tons of whales, some of which were Orcas which I had never seen before!
The way back was a different story. The boat left Kodiak at 10:00pm and we would get to Homer the next morning. The weather was bad and the seas were ~12ft and there was a gale warning. The captain ended up taking a longer route that added an additional 2 hours to the trip. We didn't think that this was a possibility. We also didn't understand that it could take up to 2 hours for our car to be unloaded from the ferry. Both of these delays lead to us returning the rental car late. Not a huge deal, but something that I will keep in mind on future trips!
You have two options for overnight ferrying. You can rent a stateroom(~$180), a non negotiable for my mom, or post up anywhere you can on the boat. This is the option I would have gone with if I was solo. You would want a sleeping pad and a bag at minimum. I would bring a head style bug net, the flies can get overwhelming, and some kind of tarp and towel to keep the moisture away from my area.

Booking the ferry is a little tough but makes sense after you dive into it for a few minutes. Here is the site that handles all of the bookings! Alaska Marine Highway
While waiting for the ferry ride back, I could tell that the weather was going to be a little rough, but I wanted to know how rough. The Windy app is all you really need. It will tell you the winds and the size of the waves! I also found the NOAA puts out a high level forecast that does not require an app download. Windy NOAA Marine Forecast
Yes.

If you didn't have a car you would be stuck in town the entire time. You can see the whole town in about three hours!
We were in a rented Toyota Rav4 and made it around just fine! The roads marked on the below map could be gravel but are well maintained.

Honestly there isn't much here. There is one main road that has a few offshoots. The first day that we were there was absolutely gorgeous so we went out to Fossil Beach and then started the drive back to town. We added the Chiniak Highway to the route on the way back! Then we drove out to Anton bay the next afternoon. Then, we were out of places to drive. There isn't a ton here if you are just looking from the car.
Biking: I freaking love biking. All of the roads outside of the town of Kodiak are 2 lane highways without a shoulder. Definitely not the most comfortable but I would ride it! It is only 48 Miles out to Fossil Beach, which would be about 80% of the entire road system!
You don't have many options, the only restaurants are in Kodiak. Here is my down and dirty review:

Some of the info on Google Maps is outdated. Some Restaurants might not be there!
After writing this I realize that there actually are a decent amount of options. Some of which may not be listed. haha
There are plenty of options to hike on the island. There are also some great spots to hike/walk/run in town! My mom and I mainly focused on the close to town hikes:

The museums are cool, but I would probably save them for a rainy day. If it somehow doesn't rain, I wouldn't feel bad for skipping!
Hanging out by the ocean for an extended period of time is the best advice I can offer. Bring a book, it is the only strategy I know!
Just go to the dump bro...

The Ferry is probably your best bet. We saw plenty from the beaches too though.
The ferry or the main harbor downtown. I was reading, Dostoevsky of course this is Russia man, on a bench by the harbor for about an hour when all of a sudden a massive sea lion surfaced. It was insane!

So cool to see some deer in Alaska. They are everywhere!

We were on the island for 3 full days and that ended up being plenty. Unless you are going for some specific purpose, I wouldn't say that you need to stay for any longer. The beaches here are awesome! The marine life is awesome! Kodiak Island is awesome!