Discover Greenwich is a new local museum which is free. Housed in a building which was formerly the stable block of the old Seamen’s Hospital, the building has been completely renovated and is easily accessible from Cutty Sark DLR: just go through the big gates with the two globes. The building also houses the Tourist Office for Greenwich and a café and bar plus a microbrewery selling historic beer (including porter) made on the premises.
These include a Roman temple, a very large Tudor palace (now almost completely lost) and the Old Royal Naval College. There is an illuminated 3D map and a large interpretative area on the Tudor palace and life inside it. his area includes a slightly strange series of speaking puppets of characters such as Henry VIII which move. There are 3D models of the palace and details of jousting. 
My favourite part was the area showing all the artefacts dug up from the site of the palace, including a bizarre and unpleasant witch’s bottle. Some artefacts have been replicated or reinstated to show features of the palace, including areas of flooring and a window. My children preferred trying on the replica jousting armour (a bit like putting your head into a large can of beans).
This area has fun bits for kids: put your head in the picture frame and get your friends to laugh. There is also a rather clever wooden model with bits of the complex: your task is to either build the college as it is or build your own version. These are nicely teamed with 17th century architects' models of the buildings. There are also display areas showing everyday life for the old sailors when it was a hospital and for officers, when it was being used as a training centre. Towards the end of its naval period, alarmingly, the buildings contained a small experimental nuclear reactor called JASON. Apparently it only made enough heat to boil a kettle.