Trekkie:

Following are some gay-friendly Brisbane hotels recommended by GALTA (Gay & Lesbian Tourism Australia). They are all "mainstream" hotels so your conservative parent will be very comfortable.

The info posted below is from http://www.edirp.com , a new gay-owned online travel agency that supports organizations working for LGBT equal rights. They offer online booking.

Conrad Treasury Brisbane
http://www.edirp.com/hotel/10190696.html

Summit Central Apartment Hotel
http://www.edirp.com/hotel/10206646.html

Hillcrest Central Apartment Hotel
http://www.edirp.com/hotel/10206647.html

Westend Central Apartment Hotel
http://www.edirp.com/hotel/11270665.html

Oaks North Quay
http://www.edirp.com/hotel/10206424.html

Hope this helps,
Oaklawntraveler