Sounds like it happens quite frequently with you and with multiple kids each time. Not that case for us. Honestly, most of the time we have done things that require admission fees (over a couple of dollars) it was just my two kids. They always played great together and enjoyed each other's company. I have (and always have had) a vehicle that seats 5. If our family went, we could only take one additional child. So it didn't happen that way very often, because then the other child was in a "left out" situation... and we couldn't invite TWO kids (one for each of our kids). No room in the car. --When they were little, obviously.
As teens, they tend to figure out their own plans, and as such, "I" am not so much inviting, as "they" are planning... so they usually have their own $ figured out. If it is a situation that "we" are actually inviting, then it is on me/us. But those are usually more reserved for bigger occasions, not just everyday type things. Birthday: waterpark with your friends.. admission on me. That's $20 a head. Plus drinks/snacks at the pool, parking fee to get on the island, and transportation (we live a long way from town). Or movie and sleep over... Movie tickets on me, with $ for some shared popcorn and then back home for pizza and whatever else during sleep over. Most kids front their own $ for the movies. They aren't cheap. (especially if they opt for the 3D showing... those are $13 each) Other parents invite my kiddo out for this stuff, too. I pay her ticket and popcorn/drink (she won't drink soda, so will either buy a bottled water, of sometimes she already has one in her backpack bag---she's a marching band kid. They ALWAYS have water on them.)
We don't do a lot of going to the park or pool.. we live in a quiet neighborhood with lots of trees and wildlife, and have our own pool. There's no admission. Come on over and bring your swim suit. I've got plenty of towels, you don't even need to bring one of those. Just your suit.
Or, in the summer, the nearby touristy island has "movies on the green" on Saturday nights. I've taken my daughter and her friends out there. The movie is completely free. Just spread out a blanket and enjoy under the stars. A little like the old fashioned drive-in, only it's a walk-in, and it's free. Bring your own snacks/drinks. Coolers are everywhere.
We live near the beach. That's another option here. Taking kiddo and a friend to the beach for a few hours. No $ required. But if we go through DQ on the way back home, it's my treat. :)
BIG stuff? We haven't done it. We are a family of 4. Anything that requires an overnight stay, we aren't getting 2 hotel rooms. My son did an overnight with a friend to an amusement park when he was in elementary. They had one child going, and invited him to join their son. I sent $ for admission, plus dinner, snacks, souvenir, etc. I wouldn't have wanted them to pay for that... even though they offered.
So, no, I don't think you are cheap. But it does sound like where you are located, things are done a little differently. Where I am, there aren't as many parents dragging extra kids around with them to paid excursions. The nearest zoo (for example) is an hour away. Not in the same town, and actually across the state line. Most people do not live within walking distance of each other, nor of activities. Everything is a car ride. And just picking up 1 additional kid can add 30 minutes to the process of doing whatever it is, simply b/c of added car time for picking up all the way on the other side of town, or in the other end of the county. MANY times, our daughter has slept over for simple movies, b/c of the logistics of pick-up distance. Same with her friends. If you drive them here to drop off, I'll bring her home in the morning. Or vice versa. Or I'll drop off, and pick back up in the morning. Two 50 minute (one way) round trips in one evening is just too much.