Taxis are everywhere in Beijing city so you should have no problem to move around.

Hotels in Beijing are not cheap (compared to the local living standard). Of course you still can find cheap accommodations but may not be of acceptable international standard. My recommendation is Landmark Hotel (the last I know the room rate is around USD60). I think it is partly owned by Singaporean (why support others while you can support you own countrymen). Also, the HRC and Passion are just nearby.

The popular hang-out for locals include Banana disco.