If you go to Pinang bus station, which is about 10kms west of Medan city you can take buses to Banda Aceh in the west, which is the Islamic stronghold of Indonesia. It is a 9 " 10 hour bus ride but worth it to be amongst a very different type of local peoples. This province is recognised as a special religious zone by the Indonesian Government " much like Yogyakarta. The Acehenese have an amazing history and it is worth reading up on this before you go and while you are there. It is very relaxed part of Indo and I stayed at a decent place called Losmen Palembang on Jalan Khairil Anwar in Banda Aceh city for next to nothing.

There are some great places to visit near Medan and I would encourage you to see anything rather than stay in Medan. If you head to the Amplas bus station to the south of Medan city you can get on one of the regularly departing buses that head to Parapat on Lake Toba. Lake Toba is the worlds largest volcanic lake and is quite amazing. Pulau Samsoir is the touristy island in the lakes centre. Try to get away from the main hordes of people " there are plenty of losmens (cheap accommodations) away from the main area - where you can relax and still enjoy yourself by hiring a bike and taking a huge ride around the island.