The docklands travelodge is very nice but a bit of a walk from the DLR (London City) but it shouldn't take more than about 10 minutes as the DLR station is inside the airport iyswim. The travlodge right next to a storage unit (Shurguard storage) so you can't miss it. Walk down the road, cross over and the travelodge will be on your left.
I'd personally buy an oystercard, which is a pre-paid travelcard, put about £8-10 on it and that will see you through or just get a day travelcard as other people have said. There should be someone at the station to point you in the right direction (TfL staff!). Dependng on the age of your dd, you might need to buy one for her.
I don't know about the top tier of the O2 (I was sat lower down to see Darcey Bussell/Katherine Jenkins earlier this year, but the O2 is a really nice venue.