I know my LO is a bit younger than yours but here's the types of things we do, obviously you have a bit more scope with things like crayons which we can't use yet (he'd eat them!).
Free things we do: We go for walks, sometimes just around the village, sometimes to the lakes to feed ducks, sometimes over to the farm to see what animals are around or stroke the horses. We do songs/games/singing/reading together, attend toddler group (Wednesday mornings...ok that costs £1 actually!!) but thats 2 hours where he loves watching the other kiddies and joining in. We go to the park and he loves the swings. We've been out in the garden a lot the past fortnight too, just exploring the grass and daisys seems ultra ammusing to him, or we'll walk around and sit in different parts of the garden where there's a new tree to explore or a hill instead of flat etc. DS also likes to peek through the bushes and 'talk' to the boy next door if he's out playing. We'll take the rocking horse, ball pool, walker etc in to the garden too. We visit friends with babies of similar ages to play or on rainy days we just stay home together with our toys and sometimes I might pop the television on for a few minutes too on the baby channel or something.
By 13 months you can add more to that, drawing, simple crafts, baking things like rice crispie cakes or have her help with say mixing the dumpling ingredients together if your doing stew or what ever. I'm sure if you have a local farm or something they wouldn't mind (if you asked) if you fed the horse a carrot or watched the chickens etc - so much costs money though, i.e. Friday we do swimming lessons, but you can borrow library books on things like toddler crafts/baking/activities etc and there are always suppliments in the local newspapers saying about local things to visit. Museums etc tend to be free entry which could be an idea? Go look at the big dinosaurs or something?
Will be interesting to see others suggestions on this too.
ETA: Also we'll go down to the beach every other weeeknd or so. It's half pebbles, half sand so even on colder days it's fun to explore but again it's a change of scenery and something different for LO to see, do and explore. Were fortunate also to have a local steam railway which we visit and the national trust have some great sites, i.e. windmills that are usually free to look at.
). We sit and build towers with his bricks and he knocks them flying, now the weather is a bit nicer we spend a lot of time in the garden and he has his swing and slide and I take his rocker, trampoline and ball pool out there too.
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