Lived in two cities and a rural village whilst DC's were little so have had various favourite places and things to do.
Mainly we did toddler groups. I have always made friends from antenatal/toddler groups and met up for park visits and play dates at each others houses.
We have had season ticket for botanical gardens. Season ticket for cheap stately home Park which had playground and water play.
Visited free museums, libraries and art galleries. (Yes even with little kids, just going for half an hour is a trip out)
Free paddling pool at seaside resort.
(Also beach etc)
Church coffee mornings and fetes
Bike ride (as in the kids on ride ons) takes an hour to get to the end of the road, but in their heads that's a trip out, then you turn around and go home!
Walk alongside river (pushchair and reins if needed)
Walk to town and back again (to buy the one item you need!)
(In cities:) played in walk-in fountains, ran riot wandered through the cathedral. Looked at stalls in a market (and tried free samples at farmers markets)
Watch, diggers, dumpers, cranes, road drilling men. Lorries, boats etc.
(We lived somewhere with a shopping centre which had an indoor Bridge over a road. The kids spent hours racing the cars (under the bridge) from one side to the other (like pooh sticks)).