If you are just going for four days it really depends on when you are going - weather all over China can go from different extremes depending on the time of year. For four days, that is a good time to explore a major city like Beijing - one of my favourite cities in the world.
You can explore Forbidden City, the Great Wall, The Summer Palace and The Temple of Heaven in and around Beijing - all amazing places, and you can choose to see a part of the Great Wall that isn't 'touristy' you just need to ask around and usually someone can take you to a more authentic, unrestored part.
I think the best place to stay is Wangfujing Youth Hostel in Sanlitun district, I always stayed there when going to Beijing - it's in a really good location - close to subway, clubs, bars and restaurants and is really, really clean and well run. The prices are cheap you can stay in dorms (which I always do - meet the best people that way, esp if you are travelling alone), or you can get single rooms. They have free internet and helpful staff.
There is also lots of cool shopping close to the hostel - Yashow Clothing Market or you can get the subway to Wangfujing DaJie, one of the main shopping streets.
Watch out for hawkers, pickpockets and dodgy taxi drivers. Don't get taxi drivers from right outside the railway station - walk a few blocks away and flag a taxi down. Taxi from railway station to the hostel I mentioned shouldn't be more than 25RMB.
Bargain down everything to less than half if you have a European face. :P