Are you in a town? City? Village?
Dh works most weekends, so all weekend organising lands on me,
When the DC where younger, and lived in a large village/town, I'd do walk to the local park for a play, then a walk down the high street, DC bought sweets, looked in charity shops for small toys, and clothes. Then stop at a coffee shop (Was a lovely independent child friendly one, so one coffee and a couple of milks, cheap as chips) Sundays I would visit family.
When DC were Slightly older in a little village. They'd play out with friends, or we'd do a small picnic and go for a bike ride, to local nature reserve. Visit friends in the village. Or take DC swimming, they had various clubs I found them to do on a Saturday, usually with digging about you can find cheap clubs. At one point DC went to a gym club, that was 2.50 for 3 hours! On a Saturday morning. Five aside football training 2.5 hours £5 . they were pay as you go so if I didn't have the money that week they didn't go.
Kids club cinema depending on which one it's was either a £1 or £2.
I did have a car so would regularly just bung them in and drive, more often then not to a beach, come rain or shine.
Walks along river banks/ canals
Museums.
Garden centres, buying a plant each to plant and grow in pots when we got home.
Baking is always good, my eldest now will just announce he's board and then says, I think I'll bake something. he is currently making a chocolate cake whilst he waits for some new game to download
We also use to do a kind of "come dine with me" "master chef" thing were it was someones turn each weekend to come up with a started, main, pudding, they had to prepare and make it all, (with help when younger)
Also my DC are teens now, but can still be enticed to do craft stuff every now and again, you can buy alsorts of get them interested, build you own kits etc..... Wilkos is good for cheap craft sets.
^They were all my on budget stuff I did, I've probably forgotten a few.