The museum isn't just pictures, they have loads of fantastic interactive pieces, some specifically tailored for children. Recently they had an exhibition on Charlie and Lola. Well, on the author of the books actually, but my dd didn't get that . They also have a room set aside for colouring, glueing etc etc (on the ground floor next to the big stairs). Go and give it a try, it's fab!
Then there's Techniquest, though I would advise going on a Toddler Day to avoid being trampled by the older children. A 10month old may not get much out of it, but she will enjoy it a lot as she gets older.
Then there are classes like JollyLiz mentioned. I can personally recommend the Music With Mummy classes - it's great fun.
Also local Mother and Toddler groups, a great way to pass an hour. There must be one local to you, usually in a church hall or community centre.
Finally there's Cafe Junior and Bambeans. Also Parc, but it's not that much fun for non-walkers.
When the weather gets better, it will be much easier to keep baby occupied as you will be able to walk to the park, or go to Roath Lake to feed the ducks.
Hope you have fun with your dd