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Many international visitors to Ramallah come to get taxi rides to see the protests in the neighboring villages (like Nabi Saleh and the world famous Bil'in protests) against Israel's separation barrier. Hostel in Ramallah has different tours, twice per week they organize trip to one of the protests and Hebron city. Keep in mind that you would protest at your own risk.
While not resembling any 'Medina'-style old city, several churches and mosques can be found that may be of interest to visitors.
A protected and family-owned building and a Historical Museum. One of the top sights in Ramallah, displaying the history and art of Ramallah's past and present. A nice and helpful host takes care of the place with over 250 years of history. Also, you can buy special souvenirs.
The museum is in the building where Arafat was held under siege by the Israeli Army in 2002. The museum is interesting in a way that it displays the Palestinian, sometimes a little questionable but interesting view of the difficult past.
The Mukata'a is a two-block compound with a white tower that is lit up at night and visible from most parts of the city. It contains some government offices and conference rooms, as well as the above mentioned Yasser Arafat's mausoleum.
The main venue for performances and concerts within the city.