well I can give you an adress for Cusco as well as for arequipa. Both hostals are very near to the plaza des arams and you can park the bike in the hostal, so it is safe.
Hostal “La Reyna”
Calle Zela 209
(Next to Sta. Catalina Convent, which is about 3 quatres from the plaza, just follow Jr. Sta. Catalina about 300 meters then turn right and cross the streeet. You shloud stand in front of the hostal then)
Tel: (0051) 54-286578
GPS: S16°23.707 W71°32.154
right next to the Cafe,Restaurant YAKU MAMA
Romms are quite good and youz have no limit of hot water!
Price: 24 Soles/2 Pers.
You will find it in two ways: by foot: follow the small little street called "procuradores" (to enter this road you need to have one big church in your back (called La Compania) and the other side of the plaza and one to your righthand side) and at the end just on the opposite side of the walk you will find that hostal. It has an Internetcaffee included and the will have to open the big wooden door to let you in with thw bike).
By bike: exit the plaza and follow the road called "Plateros" until the first entry on the right hand side, enter that small way (called Tigre) and turn right again at the next corner. then follow around a leftturn and you will find the hostal to your left before a stair.
In case you want to visit Machu Picchu you can leave your bike at the hostal, it is safe. Ask different agncias for prices, and dont accept the first one. We were two and got there for 65Dollars/Pers. includinf Train, hostal in Aguas Calientes for 1 Day, and the entry to Machu Picchu as well as a Taxi driver from cusco to Ollantaytambo who told us averything we needed to know about all the ruinas.
Back transport from Ollantayxtambo by bus (cheap).
Have a nice trip