Sitka displays its Russian heritage in many ways, the most predominant of which is Saint Michael’s Russian Orthodox Cathedral at the intersection of Lincoln and Matsoutoff Streets; and by intersection, I don't mean on one of the corners, but right in the middle of the street. As you drive by, remember to make that right-hand turn at the proper time or you will in inside the church! The church was built in 1848 and rebuilt after a devastating fire in 1966.
The Sitka National Historical Park, located to the east of the marina and within walking distance of the pier, contains an old growth rain forest with Tlingit totem poles placed throughout the park. Walking through the park and continuing further east you will find the Alaska Raptor Center which rehabilitates raptors from around North America.
For those who would prefer to explore for marine wildlife, Allen Marine operates cruise and independent excursions that go out into the Sitka archipelago to look for seals, sea lions, whales and huge rafts of sea otters just floating about in the water. Of all the ports in Alaska, if you want to see sea otters in any numbers, this is one of the best places to do that.
This is a port that is quite easy to explore on your own and the relatively compact size of Sitka makes most of the things you want to see within walking distance of the pier. If you would rather not walk the entire way, consider taking a bus tour to the raptor center and then walking back to downtown via the National Historic Park.
As a side note, Sitka does not have berthing facilities for cruise ships so all passengers are tendered in to shore. The harbor is well protected so there is little chance of heavy seas preventing or interfering with the tendering process but those passengers with mobility issues should be aware of this.