Since you have paper, get a book on origami for kids.
Many have varying levels of difficulty so that older children are entertained.
Books like mad libs are popular and fun.
Card games are great if you have multiple children at one time. If generally you have 2 or less, don’t get them. Games like UNO are fun but frightfully dull with 2 people!
This said, buy cards, esp at yard sales. They are great for building stuff. They can be cut with slots for younger children to build with.
Dominos are great to build out of.
If you have space for a box, you can put all sorts of things in it: corks, clothes pins, wire… Junk drawer stuff. Kids build the best things and they can take it home as a souvenir!
Maybe pick up a couple of yo-yos for the older kids? Old school, assuming they still make the things, no mess, and if one of you remember–or maybe google up–how to do things like “walk the dog” and other tricks, the kids might get a kick out of it.
Marbles? Again for the older kids, but good clean fun…
I was going to suggest something like this. It won’t do for small kids, but my early teen nephews will still sometimes still get these out, even though there is a housefull of toys and electronic games also available.
Our collection includes a handful of small stuffed animals, a couple of Matchbox cars, a Tonka truck, a marble run, a couple of card games, and some National Geographic type picture books (small kids can try to find the giraffe, bigger kids can read it on their own).
How about a different one: puppets. Let 'em make up stories and new personalities. I even got my little girl a “build your own monster” puppet with body parts that attach with velcro. Here’sa fewexamples.
Edited to add: if you’re really concerned about price, don’t take suggestions, hit garage sales and just buy whatever catches your eye. You can get a ton of toys for very little money.
Qwirkle is a fun game that is accessible to the upper half of your range (and to adults) - and the tiles are fun for the littles to play with like blocks.
The obvious answer. Inflatable, so it won’t take up to much room when not in use; safe for kids of all ages; safe, for kids playing around furniture; entertaining for users and observers; and most of all, hyper-cool.
Get some crayons and a bunch of these. Fold up flat, reusable, recyclable, they can become a castle, race car, robot, hat or a convenient playpen for the little ones.
All my suggestions have been covered, Just want to say that you are a very good person for doing this. Almost all my cousins are at least 10 years older than me. Visiting aunts and uncles mostly sucked, as there were no other kids to play with and I was always bored stiff.
Oh, I did think of one great thing not yet mentioned: A large friendly dog who likes to fetch.
Someone upthread said boxes. Someone else said markers. I’m gonna say get empty boxes, and maybe give the kids some washable markers, as well. Most kids from toddlers to gradeschoolers will be more than happy to play in boxes, and will love to mark them up as well. If you feel VERY ambitious, cut a door and a couple of windows in the box, so that when the box is open side down, it forms a house or fort. But just a big empty box is fun, too.
Wooden or plastic building blocks are fun, too. The downside is that you have to pick them up.
Legos are fun, but they’re expensive, and you have to pick them up, because if you don’t pick them up you’ll step on them and they hurt. Plus, of course, they aren’t recommended for toddlers.
Now there’s an idea: crafts. Construction paper, glue, paper bags, pipe cleaners, googly eyes, pompoms, paper plates, macaroni, buttons, glitter. Kids love making stuff, and the materials are darn cheap.