Any recommendations on budget places to stay that are convienent to all the tourist trips or metro? There are so many to choose.
Possible places
Beijing Eastern Morning Sun Youth Hostel
Beijing Downtown Backpackers Accommodation
Far East Youth Hostel


Another one would be City Central IYH. I assume you're looking for a dorm bed, not private room.
Cheers!

Down town Backpackers is great.... also the REd Lantern
We've stayed at both and found the service fabulous. REd Lantern has a bit more estetic appeal as it is built from a traditional style with a covered court yard in the center.
Backpackers is more like a hotel in set up.
The people at both are extremely helpful and that is putting it lightly

To make it more difficult, I stayed in the Far East International Hostel. Looks a bit like a fancy hotel when you enter, but the dorms, showers, breakfast is great!!
Having stayed at both Beijing Downtown Backpackers and Far East Youth Hostel, I'd recommend the former over the latter. Friendlier staff. More interesting neighbourhood.