My PFB is also exceptionally amazingly wonderful, highly intelligent and generally an all round genius (she's 2.5). We do actually think she is the cleverest, best toddler who ever lived but also aware that we may be slightly biased 
. DH, my mum and I share her care and I really think that she gets a lot from, for example:
Going to groups and spending time with other children - there is loads to be learnt about how we interact with other children.
Visiting other mum friends with children. As above.
Going to the supermarket with me. We chat when I'm not knackered and/or she's not being a pain in the neck about all sorts of things: what we are buying, what colour everything is, what we are doing later, she's even started spotting letters of the alphabet on the big signs saying "fruit and vegetables", "milk" etc.
Going for a walk anywhere (the local street, the park, a wood). Loads to talk about - the types of cars, the birds, the trees, anything at all which she notices.
As others have said, helping with things around the house - DD loves baking, cleaning 
, attempting to wash up - anything really.
I do try to answer her questions as accurately as possible whilst keeping the answers appropriate to her level of understanding. You can usually find some sort of answer to any question. Although it's often "let's look that up on the computer" when I don't know! We've looked at all sorts of interesting things that way (eg the sound of a kookaburra, what owls look like, etc).
If you're talking about more "formal" learning things like counting, the alphabet etc - it's very very easy to build that kind of thing into anything you are doing (eg DD spotting letters on supermarket signs, or car number plates, or spotting road signs which are circles as we drive along, or spotting the next red car, or counting anything at all). And there is so much which you can teach her beyond this, about how we are kind and polite, and how we cross the road, and how we share, or deal with other people, or deal with our own frustration or anger.