This is written from my head with just memories to work from - if there is something you would like to add in the comments please do, and welcome.  Or if it is something that should be included in the article then please just let me know and I shall

edit.
It gets increasingly easier and harder to find interesting and fun activities as your child gets older.  TAC comes in very handy at this age.  See the group Total Attention Challenge, as well as advice that has been written and is linked (see below).

Internet colouring pages; The ultimate colouring book - there are millions of places to get pictures, educational as well as fun ones.  I keep all of hers in a folder as most have been educational on somelevel - mostly learning about animals so far.

'School time'; encouraging learning, ABC & 123.  Use whatever tools you can. 
We use 'Numberjacks' Tv program, numbers on signposts, cars, buses etc
We got her a toy bus with numbers and letter on it when she was 1.  Now we use it as it is intended
We practice writing
We use sticker books and various other activity books that help develop skills that she will use in school

Cooking; she is quite the gormet chef these days - or so she thinks.  She was making pizza the other day and just grabbing handfuls and sprinkling over it.  really reminded me of those TV chefs my parents watch sometimes.

Gardening; E has had her own and has also painted the garden fence with her Papa. Many little jobs that can be done by little ones - just gotta think about the ways to make it possible instead of the complications. 

Drawing; E has a diary that she can draw/write in any time, this includes shopping lists and birthday invitations in her latest diary

Water play; this has included car washes and watering the garden now.

Reading; she has always read, but now she makes up her won stories more and more and they actually make sense as she tells them to her dolls at their bedtime.

Magazines are a great tool for ideas, activities for quiet time as well as joint learning time.  they often also come with some kinda toy, sticker collection or attachment that will also provide hours of fun!  We limit them to one a month in our home (if that) because there is so much use we get from them and they usually end up strewn around the house within a week also, so it takes us the rest of the month to make sure we got all the bits, that we have read and done all the activities and that the magazine is finished before we go buy our next one.

Pre-school;  If you can bear to let your child go for a half day this is well worth it.  It pays dividends in the social life of your toddler and they come home with such independence.  It is awesome.  It still stuns me, and she was in nursery from a young age when I attempted to work....lol.  But we have done various things in our time,and each has benefitted her differently and she grows so much in a different environment where I am not controlling every little thing for her. 

Finally 3rd Birthday Party;  What to do?  We had another teaparty!!!  And we also look t be having one for her fourth birthday!  The colour scheme still stands, but the cake changes shape this year and needs different colour icing to last year.  In our case she didnt want friends again - just family.  So it was cheap and simple for me.  Always remember;  It is up to you what you do.  You have nothing to prove, only to do the best by your child, which really should be our everyday wish and dream anyhow.  So see what you feel up to doing, what can you afford (realistically) financially and time-wise?  Offer your child some choices based on the musings you have had and refine it into the ultimate party for your child and yourself.  An adventure play area that caters for parties and you just pay the money and they do the rest is a fantastic option if they want to bring along all their friends. 

Wishing you lots of love, fun, gales of laughter and wonderful amazement as you watch your child develop and join the dots in their minds.
Peace
EF.x