There are classes for the 3-yr-old, music, gymboree, yoga, that kind of thing. You can bring the 10-month-old along. Also, storytime at the library. We don't have TV anymore and we don't miss it. Read to the kids, they can play together, go for walks, to the playground, take them out to lunch if it's not too hard, playdates, art projects for the older one...
If your kitchen is tile/linolium it is great to give them paper, crayons, markers, paint and let them go for it. If you have any boxes of loud toys those usually work pretty well. At that age they hav dso much imagination.
coloring,painting,play outside,go to the park,walk the dogs and make playdates with my best friend's son. sometimes I even spread my errands out over a couple days to have something different to do everyday
Coloring, play-doh, finger painting, board games, build a fort, line chairs up and pretend its a train or whatever, hide and seek, bake something, my son loves for me to put vinegar and baking soda in a 2 liter bottle and put a balloon on top and watch it blow up, go to the park, play outside. There's many things to do.