At three we got our daughter some V-tech toys, some of the simpler ones that are usually on amazon for 20 or less. One my daughter loved and it really helped her learn to write with ease (because it gave simple instructions) was the Doodle and Draw. I just saw the receipt this week when I was cleaning out some drawers it was 17 on amazon, she would play with it forever and so would her friends. The battery life seemed to be good too. We also got her the orange lap top from them, she liked it more when she was four though.
Something I have done for ideas for gifts for her (she is 5 now), was went to toysrus.com, amazon, etc and searched learning toys for 3 year olds, etc. If you look them up, you can find reviews which I found to help a lot.
Don't forget games like hi ho cheerio, which teach waiting your turn and counting. Uno is a great one, even though it states it is geered toward bigger kids. Little ones can get the concept with help and only 2-3 players and the bonus is that it reinforces colors and numbers-which is a great learning game. Memory too of course.