I received a similar question on my website, Ask the Mediatrician (http://bit.ly/2n18m), and I thought this answer might help you.
The most important developmental task children your daughter's age is not to learn fact (which is what computers teach) but to learn how to learn. Computers really only provide tasks with right and wrong answers and thus don't encourage the kind of problem solving and logical thinking necessary to build flexible learners. Instead, they teach kids to memorize and to be afraid of being wrong. That fear is a problem because you want your daughter to take risks in learning. You want your daughter to try things out, say new words, and play with toys in new ways. She needs to build that creativity and love of learning far more than she needs to learn computer skills.
Some ideas for options that encourage your daughter to "learn how to learn" are open-ended, creative play options like modeling clay, markers, paper, books, musical instruments (like maracas or tambourines), a sandbox, or a building set that allows her to build free form things. From what we know about brain development at this age, these toys will help build stronger, more flexible brains than any electronic toy will. Computers are wonderful teaching tools for kids 3 and older. You will want to introduce them to your daughter at the time when they will do the most good and not run the risk of her being bored and uninterested at 3 because she was frustrated at 1 or 2.
Enjoy your media and use them wisely,
Dr. Michael Rich, The Mediatrician®
I have an 18 month old son and I totally know what you mean about keeping them occupied! My little guy has always been super active, and it's hard to find a way to keep him busy, even so I can just make dinner. We don't do much media in our house, but here are some things I've found that he loves in the past 4 months that give me at least 15 minutes to get something done:
--a box of cheap macaroni, 2 big pots and a big spoon to transfer the macaroni back and forth
--a little tub of water, some soap, and his alphabet letter magnets placed on a giant towel in the kitchen, also with a big pot and spoon
--going for walks outside where i carry a big bucket and let him place anything he wants in there (pinecones, acorns, sand, snow)
--he's really into music, especially the MusicTogether CD's, just perfect for this age.