After getting off at Keleti, you will have to get on the metro, and take the red line towards Déli. Make sure you buy a single ticket, it will be enough for the entire journey. Get off of the Metro at Deák tér. Get on the Blue Metro and go to Arany János utca. When exiting the metro station start walking up Andrássy utca towards the Basilica. Andrássy utca will cross Bajcsy-Zsilinszky utca, and you will just have to walk a few minutes to get to the Adagio hostel under Bajcsy-Zsilinszky way 17!