Seldovia
From Homer you can take a water taxi across the water to Seldovia or you can take a 15 minute air taxi. Seldovia is built on the water and has, maybe, two restaurants and a bed and breakfast. It simply has a great feel that is hard to describe but my wife and I considered getting married here (but decided it was too tricky to get too.)
Where to Stay: Tent and Breakfast offers just that – a tent and breakfast. Might double check to see if you need to bring a sleeping bag.
Here is a link with other options – the place we used to stay has sadly closed.
Hiking: There are a few roads over here – you can probably bum a ride to one of trailhead – and heaps of great hiking in Kachemak Bay State Park (a place that should be a national park in our opinion.) But again, call around first to find out about the snow conditions if you’re heading out in late May or early June. REI in Anchorage rents snowshoes.