Toddler Activities  

I'd highly recommend getting flashcards to start teaching her her letters, numbers, and colors - even as young as she is, it's possible for her to get it. My son did very well at that age in learning his letters and such. Make it fun for her; we use sticker charts here. Every time she learns a new letter and can remember it, you could let her put a sticker on her chart - it's very inexpensive and it worked so well with my kids - it made learning fun for them.
It may take her a while to start remembering, but don't be discouraged - you'll love the results when she starts catching on!

How about making some playdough (as long as she doesn't eat it...) you can make it whatever colour you like and/or add glitter. You can make 'gloop' with cornflour - it has a wonderful texture but isnt really messy. If you can get some shredded paper, you can put it in a box and hide small toys for her to 'find'. She could probably do crayon rubbings if you held the paper still for her and you could roll marbles, cotton reels or plastic trucks in paint and then across paper for some abstract art work! Painting with water on your outside slabs is good or you could do some floating and sinking experiments or use a simple balance for heavier/lighter. A 'feely' box or bag is usually quite popular or things with different textures. All these things give you the chance to use lots of new vocabulary which she may not be able to say as yet but she'll recall later on. You could make one of those magnetic fishing games or let her decorate biscuits/cookies etc. Whatever you do I'm sure you'll both have fun

i dont have kids yet but i used to work in a preschool setting so thinking of activities for kids is something that i used to do full time...
you can mix fruit or veggie salad with her, you can do handprints/footprints in different media (paper, cloth,wood,etc), you can also tear, crumple, fold or even cut (introduce her to the use of scissors) and do all kids of things with paper, this will improve her fine motor skills. you also make a project together -paper mache is easy,or macaroni shell crafts(you can string it like beads or make collage out of it).
gross motor activities are also fun. you can scatter plastic balls around & ask her to pick it up, crawl under lined up chairs and do an obstacle course out of huge boxes.
there are tons of activity ideas that you can find online. There are also books that compile 365 days of activities for your toddler.
'ope this helps.

I would suggest you to buy her colouring books or take printouts from the internet and make her colour those pages. building blocks was also quite engaging for my kids, they spent hours trying to make a ship or a dinosaur . also I had bought them a leapfrog infants laptop, it was really very educative, my daughter was able to identify alphabets and numbers even before she started her play school because of this laptop, it has this interactive key and mouse which lights up as we move them. it was worth the money. I still have it after all these years, my daughter is 8yrs now. It is a hit with all the kids.

I have a 2 1/2 yrs old son and I am also like you. I never stop thinking of what activities to do in order to make my toddler busy and spend quality time with him. I bought him educational books, the colorful ones. Books for ABC's, numbers, animals and shapes. I let him explore and at this point in time he already knew the contents of the book I bought for him. And, I am still buying new books for him until now. We also spend some time watching dvd's of nursery rhymes and some selected kiddie movies. He knows already the story of Lion King coz he's watched it several times already. Be sure that you screen the movie first before you let you toddler watch it.

We do colouring and painting, and my daughter also loves to do jigsaw puzzles. You can get suitable ones for two-year olds, and it really keeps them occupied, they start to think logically about which bit goes where and why, and trying to fit the pieces together develops their motor skills.

You could also do some baking with your daughter. I haven't yet baked anything major with my daughter, but I get her to help me whisk eggs, put pasta in the saucepan and other little tasks like this. It's lovely to let them feel involved in things like this. I'm planning on making a chocolate cake with her; it will be messy, but hopefully fun! My cousin suggested rolling out pastry and making biscuits, as she'll be able to use cutters to make different shapes. It would also be really good fun to make simple types of treats, like chocolate rice crispy cakes.

Lego (or other building toys) is also a popular activity. Anything you can use to build a tower (like blocks), or make things like cars, buildings or flowers! You can also make these activities educational by counting the bricks as you put them on.

Another very popular activity with my daughter is gardening of any kind. She loves weeding(!), planting plants or seeds, and watering things and picking anything that grows and can be picked! Even if the weather's not too great, you can always get some trays and plant some seeds indoors. Then she could be in charge of watering them every day. She could watch them every day and learn about how seeds grow into shoots, then plants and then flowers.

i have a two year old child too but he is a boy. we play ball and ride the bike. we also watch together, draw together and run outside together. when it rains we like to bathe together under the rain. i wish i can give some suggestions to you but girls activities are different from guys. sooni want him to learn how to plant so next year we will both try to plant tomatoes. why not try to cook or bake together. she can put designs on your cookies.

What about playdough - you can make your own. You can make you own book. You can make one with textures, shapes, different numbers and letters. The fun part is finding things to paste in the book. You can make pictures out of dried beans or seeds by pasting them on a paper plate or cardboard. String cereal onto a necklace like fruit loops. You can make your own grocery store by saving carboard container from food our plastic containers and set up a store for her to shop and then play with. Chalk is great outside. You can trace her body and then you can both make a face and clothes and she has a lifesize picture of herself.

I know you may not like this idea, but have you ever tried fingerpainting with pudding? It's great for toddlers because it has a different texture than regular paint and it's completely safe so if she decides to stick her fingers in her mouth, it's just pudding and nothing else. Plus, it has a great smell too which is excellent for toddlers since they learn through their senses.

Jogging in the morning, I play my guitar while he dance and sing. Browse the computer together. Play games on my PC together. Do the groceries with him and lets him choose what he wants for that day. We do wrestling as well.

Actually, I don't have any specific activities for my son, the moment I think of something interesting, he'll surely love it.