The local library often has a rhyme time and a toddler tales story time, if you are within travelling distance of more than one library you will have more options of what day to go. I found I always needed to go out at least once in the day, even if it was just a trip to the local corner shop to buy a bottle of milk. Is she walking? If she is it's a great time to start shopping 'training' just go for one item, let her walk around the shop and get used to looking and even touching some safe things under close supervision whilst you do not need to buy anything. Maybe buy a tub of blueberries or something for her to carry and pop on the check out, then eat them when you get home. Honestly my single item shopping trips with DS were well worth it. With no stresses and the shops quiet because most people are at work etc.
Trips to:
electrical appliances shop (to be amazed by washing machines and vacuum cleaners!)
pet shop (to look at hamsters and live crickets etc in tubs, fish etc)
garden centre if you have an indoor one nearby
fabric shop
...basically at that age they just love having the time to look at everything, it's all new and exciting. Clean her hands so you don't worry about her touching things and the experience becomes even more amazing to LOs
at home
building blocks
reading books
play doh
sing songs
make home made musical instruments (pasta or rice in seal tubs, pan lid symbols, pan drum with wooden spoon) and start a band!
'painting' with jelly, yoghurt, ketchup, mayo, gravy - either dip fingers/hands into tubs then paint/print onto paper or just spread some on a baking tray and let her make marks in it with fingers or brushes/sticks - all safe if she eats it
messy play - can of spaghetti emptied into a big tub or the bath and let her go wild in it! same pack of cornflakes or rice crispies for a crunchy experience
peek a boo and hide and seek are good games for any age and really help with any separation anxiety as they learn things/people are coming back. For hide and seek hide yourself in view first. Use a toy or teddy to 'hide' in view and just get her to look around the room for it, then half hide it if she is ready for the next level. Lots of fun!