What are the ways except toys and books in which I can engage my 2 year girl so that she can learn and play both?

I have always looked for outdoor activity for my kids. Not only is it healthier and more engaging for the LO. Jacob Ballas at the botanic garden is a good place to try out. You may want to consider that. A simple walk in the park downstairs is great too. It promotes, kinetic, visual and audio learning. Great alternative even when you are on a tight budget. Plenty of things to learn, and even to engage in a communication with your girl. Have fun outdooring :)