We just returned from Olkhon Island after a fabulous stay. It is indeed a very special place. We arrived in Iskutsk after 4 nights on the train from Moscow. Although we had booked accommodations ahead of time, we had not sorted out transportation to the island.
We stayed at Irkutsk City Lodge for one night and asked at reception about transportation for the next day. They were very helpful and set up for the mini bus to pick us up... Door to door service to Nikita's! While to Russian speakers this doesn't should like a big deal... when you only know a few words of Russian , it was a stress free way to go! Cost was 750rb per person. Many hostels can arrange this service.
We spent 4 nights on the island and loved every minute- We took a north island tour with hiking from Nikita's for 800rb per person. Wonderful scenery... The road were very rough! Lunch was included as well as several scenic stops along the way.
There are several accommodation choices in Khuzhir, you just need to find one that meets your needs. Nakitas worked for us but several people we meet were pleased with this homestay choices.
We booked the returning minibus for 650rb from Nakitas to the bus station. Had we walked to the tourist information center with our luggage it would have been 600rb. A guide we meet at the ferry crossing told us that the big bus... More comfortable than the minibus was only 500rb but was slower. This Is unverified info however.