I'm happy with my Seiko 5. It was like 90$ when I got it 7-8 years ago. It took a bit for it to "wear in" but now it keeps time for months without me having to set it.

Seiko makes excellent mechanical wrist watches. What is your intrigue? I'm assuming you like the idea of mechanical wrist watches and want a timepiece that is accurate and built to last. $200 is just a little below their entry price point I believe but you can always find used watches on eBay/Marketplace and the like. If you learn a little bit more about the industry then you might be able to find a bargain and get it serviced to work like new.

I got extremely lucky when I was fixated on the idea of owning or restoring a mechanical watch when I learned that my grandfather left behind a 1930's Hamilton. Nothing super high end, but a watch that would probably go for $600 today and was my style. I find it hard to match my style today because it seems everyone is searching for a massive statement piece on their wrist. I just wanted a watch that ticks when its quiet, has character, and can be passed on to my own children.

I have an Original Grain watch that I like a lot. Not too expensive.

For a skeleton watch, yes.
For a mechanical watch, also yes.
Unfortunately, prices have gone through the roof in the past few years.
Now I don't think there are any nice quality watches left in that price range.

You can still get a Vostok Amphibia for that kind of money, which is entirely hand-crafted, definitely interesting mechanically, and will last decades. But buying from Russia at the moment (on a Russian website), waiting a month for delivery, and getting the Vostok experience isn't everyone's cup of tea. Also, I don't think it's even possible to get them shipped to the US.

Even a nice Quartz watch like a solar-powered Citizen Eco-Drive will be slightly out of your budget.
If you still do want a mechanical watch, look for Seiko, Citizen and Orient. Those are the best budget offerings.
Chinese Red Star watches also fit the budget, but they're also not for everyone.

Some companies have mechanical watches in the 400-500€ range that can go for 200€ used. I have a Junkers that I bought used for 200€ some years ago, and it's got a glass bottom (other models do, too). But honestly, I wouldn't make this a criterion, because you rarely see the back, and skeleton watches can sometimes look tacky.

Festina. Reliable miyota movements.

If you're any dexterous at all, you can build a completely custom one that you choose all the parts for~$150. And it's the same movement they use in some $1000+ pieces.

I've got one of these, and it's the least expensive that won't get sneers

https://www.orientwatchusa.com/collections/orient-bambino/ra-ag0002s30b