There's no precise equivalent. I miss the taskpad, too the visual representation of the data files and log files was nice.
Last log backup and last full backup are on the first page of the 'properties' page for each database (right-click and select properties).
Use the following query to get the relative sizes of files (and filegroups):
You can also query the msdb database to find backup history. I forget the exact tables, but I remember that a full backup has a type of 'd' (for database, I suppose).
size * 8 / 1024.0,
fileproperty(name, 'SpaceUSed') * 8 /1024.0,
fileproperty(name, 'SpaceUSed') / cast(size as decimal(18,3))
sum(size) * 8 / 1024.0,
sum(fileproperty(name, 'SpaceUSed')) * 8 /1024.0,
sum(fileproperty(name, 'SpaceUSed')) / cast(sum(size) as decimal(18,3))
Have you hugged your backup today?